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AUTHOR: 


SIDGWICK,  ALFRED 


TITLE: 


USE  OF  WORDS  IN 
REASONING 

PLACE: 

LONDON 

DA  TE : 

1901 


COLUMIJIA  UNIVIZKSITY  LIIJKARIES 
PRESERVATION  DEPARIMENI' 


Master  Negative  # 

9.L--MP_Lfe>.r_3 


BIBLIOGRAPHIC  MICROFORM  TARGIZT 


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160 


Original  Material  as  Filmed  -  Existing  Bibliographic  Record 


i  2^^^         Sidgwick,  Alfred,  1850- 


Tlio  use  of  words  in  reasoning,  bv  Alfred  Sidgwick  ... 
London,  A.  &  C.  Black,  1901. 

xi,  370  p.    22h"\ 

Contents  —pt.  l.  The  nature  of  reasoning.— pt.  2.  Description  and  am- 
biijnity.  pt.  3.  Tlic  leading  technicalities  of  formal  logic— pt.  4.  Summa- 
ries. 


1.  I.ogi<  ■    2.  Reasoning.        i.  Title. 

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I     I 


THE   USE  OF  WORDS  IN  REASONING 


JlY  THE  SAME  ArrilOH 

THE  PROCESS  OF  ARGUMENT 

A  CONTRIBrXlON  TO  LOOIC 
Crown  8vo,  Clotb,  Price  r>s. 


'•\V\'  cannot  jittempt  atle(juately  to  snnimaiise  the  hook,  for  it 
is  itself  a  summary  of  admirable  concentration  ami  {.ithiness,  con- 
taining a  wealth  of  acute  criticism.  Professor  Sidgwick's  reputa- 
tion makes  our  recommendation  sui^ertluous,  hut  we  hope  the  book 
will  be  very  widely  read  and  studied.  It  is  a  mo^t  valuable  con- 
tribution to  the  most  valuable  kind  of  logic  ;  and  it  is  not  at  all 
crabbed  or  hard  to  read."— 'At  Wistminstcr  Gazette. 


A<JENT8    IN    AMf  hli  A 

THE   MACMILLAN    COMPANY 
66  Fimi  AvENVB,  New  York 


THE  USE  OF  WORDS 
IN   REASONING 


BY 


ALFRED  SIDGWICK 

ACTHOR   OF 

^AMAM,.         I^lsXiNCT.OS    AND   THE   CRmciSM    Or    BEUEr  ' 

IHE   I'ROCRSS   OK    AR,.,  1!FVT.     ETC..   ETC. 


LONDON 
ADAM    AND    CHAELES    BLACK 

1901 


PREFACE 


\Qb 


1  ^ 


y 


Thk  two  chief  purposes  of  this  book  will  best  be 
seen  by  consulting  Part  IV. ;  which,  by  means  of 
the  references  given  in  the  text,  may  also  be  found 
of  service  to  the  reader  pressed  for  time.  Parts  I. 
and  11.  are  addressed  to  any  one,  however  unaccus- 
tomed to  the  study  of  Logic,  who  is  interested  in 
the  distinction  between  better  and  worse  reasoning ; 
Part  111.  to  those  who  find  it  difficult  to  believe 
thai  tiiere  is  much  amiss  with  the  usual  account  of 
the  leading  logical  technicalities. 

1  have  again  to  thank  Mr.  Carveth  Read  for  the 
great  help  he  has  given  me  with  the  proof-sheets,  in 
spite  of  our  many  differences  of  view,— differences 
the  extent  of  which  will,  no  doubt,  undergo  in  course 
of  time  still  further  limitation  and  definition.  And 
1  have  also  to  thank  Miss  E.  E.  C.  Jones  for  much 
discussion  of  the  MS.  under  similar  conditions.  Some 
controversial  exaggerations  have  in  this  way  been 
avoided,  and  if  any  still  remain  they  will,  I  hope,  be 
duly  pointed  out  by  other  opponents. 


m  rt»»fr  ^mrt^m 


I 


CONTENTS 


PART   I 


THE  NATUIIE  OF  1!EAS0NL\G 


SE«  1 


CHAPTER    I 

Aim  and  Method  of  Logical  Study 


1.  The  Chief  Divergence  of  Method 

2.  Ditlerent  Purposes  of  Study 

3.  The  Assumptions  of  Formal  Lof^ic 

4.  '  Undeniable  Truths ' 

5.  Hall-Truths 

♦J.  Abstract  Statements 

7.  The  Purpose  of  Technical  Terms 

H.  Definition  and  Translation 

1>.  Can  a  Progressive  Logic  be  Taught  ? 


PAOB 

3 

5 

7 
19 
25 
30 
3.) 
47 
50 


CHAPTER   II 

Reasoning  and  Syllogism 


10.   Keflective  and  F'orward  Reasoning 
1 1     How  Conclusions  are  Supported  . 

12.  The  Syllogistic  Framework 

13.  Verbal  Simplicity  of  the  Middle  Term 

14.  Uses  of  the  Syllogism     . 

1 5.  Summary  of  the  Chapter 


58 
59 
61 
67 
71 
80 


Vlll 


USE  OF  WORDS  L\  REASONING 


CHAPTER   III 

RKA8UN1N0    AND    GENERALISATION 


t«CT. 


16.  Hypothesis  depends  on  Previous  Theory 

IT.  Verification  also  tUjiends  on  Previous  Theory 

1 8.  Use  of  the  Inductive  Mrthods     . 

1 9.  The  Notion  of  a  '  Cause ' 


CHAPTEK   IV 
Rea8^)ning  and  Judgment 

20.  A  Problem  of  Definition 

21.  Some  False  Solutions  of  the  I'roblem 

22.  Judgment  as  Process  and  as  Instrument  . 

23.  Reasoning  as  the  Advance  to  a  Conclusio'i 

24.  The  Effect  of  Admitting  the  Difficulty    . 
2f>.  The  Weak  Points  of  Reasoning  (»r  Jud«:ment 
2f).  Some  Objections  Considered 

27.  The  False  Duality  of  the  Premisises 

28.  Syllogism  and  Petitio  Prinn'yii    . 

29.  Transition  to  Part  IT.     . 


PART    I] 
DESCKIPTION  AND  AMBIGUITY 


CHAPTEK   V 
Description,  in  General 

30.  Description  involves  the  Use  of  Class- Names 

31.  All  Statement  of  Fact  is  Description 


CHAPTER   VI 

The  Nature  of  Classes 
32.   Meaning  of  the  Word  '  Clasa '      . 


PACK 

86 

89 

95 

100 


110 

112 

115 

117 

118 

121 

124 

129 

131 

13:) 


141 
145 


CONTENTS 


3ECT. 


33.  Ancient  and  Modern  View  of  Classes 

34.  False  Interpretations  of  the  Modern  View 

35.  The  *  Laws  of  Thought ' . 

36.  The  Weak  Point  in  Description  . 

37.  Metaphorical  and  Matter-of-Fact  Description 

38.  Some  Con8e(|uences 


CHAPTER   VII 
Indefimtenejss  and  Ambiguity 

39.  Complete  Description  and  Perfect  Definiteness 

40.  The  Popular  View  of  Indefiuiteness  and  Ambiguity 

41.  Degrees  of  Indefiuiteness 

42.  The  Indecision  of  Common  Sense 

43.  Indefiuiteness  as  Distinct  from  Ambiguity 

44.  Ambiguity  as  Attaching  to  Assertions 

45.  Proportion  of  Doubtful  Applications  Irrelevant 
40.   Subtlety  of  the  Inquiry  Irrelevant 

47.  The  Work  involved  in  Finding  an  Ambiguity 

48.  Summary  of  the  Chapter 


CHAPTEK   Vni 


The  Progress  of  Knowledge 


49.  Questions  of  Fact  and  of  Meaning 

50.  The  Virtue  and  Vice  of  Casuistry 
'il.  The  Function  of  Scepticism 


IX 

151 
153 
159 
164 
167 
171 


174 
178 
180 
183 
185 
187 
190 
193 
195 
197 


205 
215 
223 


PART  III 

THE  LEADING  TECHNICALITIES  OF  FORMAL 

LOGIC 

CHAPTER   IX 


Kinds  of  Name  or  Term 


149 


52.  *  Logical  Character ' 


239 


USE  OF  WORDS  IN  REASONING 


CONTENTS 


XI 


MO. 


Connotation  and  Connotative  Names 

54.  The  General  Name 

55.  Denotation 

6(J.   The  Abstract  Name 


chaptp:k  X 

Kinds  of  A^^ertion 

57.  '  Logical  Form  '  ... 

58.  Universal,  Singular,  Particular  ;  Affirmative  and  Nejjative 

59.  Essential  and  Accidental  ProjJOrsitions 

60.  Categorical  and  Hyi>othetical  Propositions 

61.  Mo<lality  ..... 


PAGE 

244 
249 
252 
253 


259 
263 
269 


272 


279 


CHAPTER   XIII 

How  Logic  might  be  Taught 


70.  A  Method  ol  Simplification 

71.  The  Class-Name  as  Predicate 

72.  Predication  and  Reasoning 
T;i.  Theory  and  Fact 

INDEX 


PAOR 

343 

346 
352 
358 


365 


CHAPTER   XI 


KiND.s  OF  Argumem,   om   Kea.^umno 


62.  Deduction  and  InducUun 

63.  Categorical  and  other  Syllogisms 

64.  Mediate  and  Immediate  Inference 


286 
289 
301 


PART   IV 


SUMMARIES 


CHAPTER   XII 
The  Case  against  Formal  Logic 


65.  The  Limits  of  the  Accusation 

66.  The  Simplification  Illusory 

67.  The  Doctrines  Unimportant 

68.  The  Obstruction  to  Progress 

69.  Appeal  for  a  Defence 


309 
314 
321 
330 
335 


PART  I 


THE   NATURE   OF   REASONING 


CHAPTER    I 

AIM   AND   METHOD   OF   LOGICAL   STUDY 

§  1- — The  Chief  Divergence  of  Method 

We  may  safely  assume  that  no  one  who  sets  himself 
to  begin  the  study  of  Logic  is  entirely  ignorant  of  the 
nature  and  purpose  of  that  science.     He  will  probably 
have  some  false  ideas  of  it,  but  mingled  with  these 
will  also  be  some  true  ones,  even  if  vague  and  scanty. 
At  tlie  very  least  he  knows  one  leading  fact  about  it 
which  will  serve  as  a  starting-point :  he  knows  that 
tlie  mam  desire  and  purpose  of  Logic  is  to  inquire 
into  the  difference  between  good  and  bad  reasoning. 
It  18  a  common  experience  to  feel  convinced  that  a 
given  piece  of  reasoning  is  weak  or  tricky,  and  at  the 
same  time  to  find  a  difficulty  in  stating  clearly  its 
aults.     That  natural  difficulty  Logic  seeks  to  remove 
It  tries  to  extend  and  reduce  to  order  our  half-formed 
opinions  about  the  diflFerence  between  good  and  bad 
reasoning ;  tries  to  weed  the  errors  out  of  them  and 
to  establish  them  on  a  scientific  foundation. 

Other  views  ■  of  the  nature  of  the  central  problem 
are  sometimes  put  forward,  but,  for  reasons  which  wUl 

See,  for  instance,  noU,  p.  47. 


USE  OF  WORDS  IN  REASONING        part  i 


appear  in  §§  4-7,  they  need  not  be  taken  as  con- 
tradicting the  statement  just  given.  A  real  conflict 
of  opinion  begins,  however,  with  the  (question  how  to 
set  about  making  Logic  scientific ;  and  the  chief 
divercfence  of  view  is  between  those  who,  more  or  less 
intentionally,  accept  Mathematics  as  the  type  of 
science,  and  those  who  do  not.  The  former  party 
seek  to  base  the  doctrines  of  Logic  upon  a  few  self- 
evident  axioms,  while  the  latter  party  regard  this 
attempt  as  the  ruin  of  Logic  from  both  a  practical 
and  a  theoretical  point  of  view  ;  they  maintain  not 
only  that  nothing  is  gained  by  it  but  that  a  false 
security  is  thereby  encouraged,  which  hinders  the 
development  of  Logic  and  which  also  directly 
obscures  the  distinction  between  sound  reasoning 
and  fallacy. 

This  chief  difference  of  opinion  about  the  nature  of 
the  study  corresponds  in  the  main,  though  somewhat 
roughly,  to  the  difierence  between  the  traditional 
Logic  and  newer  systems,  or  between  Logic  as  usually 
taught  for  elementary  examinations  and  that  larger 
and  deeper  study  of  Logic  which  is  sometimes  called 
Theory  of  Knowledge.  But  a  better  account  of  it  is  that 
the  aim  of  the  one  party  is  to  make  Logic  ti^  formal 
as  possible,  while  that  of  the  other  is  to  keep  in  view 
the  special  harm  that  attaches  to  formality.  Such  is 
the  distinction,  at  any  rate,  that  chiefly  concerns  us 
in  the  present  book.  Opposition  to  Formal  Logic  is 
a  prominent  feature  of  the  following  account  of  the 
use  of  words  in  reasoning.  And  in  order  that  the 
extent  or  kind  of  this  opposition  may  not  be  unduly 
misunderstood,  some  account  of  its  motives  and  limits 
must  now  be  attempted. 


cii.  I,  §2  AIM  AND  METHOD  OF  LOGICAL  STUDY  5 

§  2. — Different  Purposes  of  Study 

In  the  first  place  it  is  freely  confessed  that 
formality  is  only  a  defect  in  Logic  so  far  as  our 
purpose  in  the  study  is  to  investigate  the  difference 
between  sjood  and  bad  reasoninor  rather  than  to 
acquire  any  other  kind  of  (what  may  be  called) 
knowledge  of  Logic.  If,  for  instance,  our  purpose  is 
to  get  up  the  subject  as  quickly  as  possible  and  then 
dismiss  it  from  our  thoughts,  we  should  probably 
achieve  this  result  better  by  keeping  rigidly  to  the 
traditional  system.  The  kind  of  reader  here  chiefly 
considered  is  one  who  is  interested  in  the  main 
problem  of  Logic  for  its  own  sake,  and  not  merely  in 
order  to  pass  an  examination.  Our  existing  text- 
books attempt  to  supply  both  these  different  needs  at 
once,  and  inevitably  steer  a  wavering  course  between 
them.  It  seems  better  to  recognise  from  the  first 
that  the  two  kinds  of  inquiry  are  to  a  great  extent 
incompatible.  From  either  point  of  view,  no  doubt, 
there  are  logical  doctrines  to  be  mastered  and 
technical  definitions  with  which  we  have  to  become 
familiar,  l)ut  the  difference  lies  in  the  way  these  tasks 
are  undertaken.  For  the  one  purpose  you  attempt 
to  learn  them  like  a  lesson  ;  for  the  other  purpose  you 
attempt  to  explore  them  more  thoroughly  and  at 
greater  leisure.  The  candidate  for  examination  wants 
the  doctrines  laid  dow^n  by  authority,  as  definitely 
and  decisively  as  possible,  and  he  wants  the  technical 
definitions  short  and  final ;  doubts  and  difficulties  are 
a  mere  hindrance  to  him,  except  so  far  as  he  can  learn 
that  there  are  two  opposite  schools  or  authorities  both 
of  whom  it  is  w^ell  to  quote  or  mention.  He  is  always 
under  temptation  to  simplify  the  subject  by  assuming 


i 


6 


USE  OF  WORDS  IN  REASONING        part  i 


that  it  is  an  easy  matter  to  establish  the  general  type 
of  correct  reasoning,  and  to  catalogue  the  departures 
from  it  which  are  prevalent  or  possible ;  and  that  to 
master  the  use  of  the  technical  terms  recjuires  only 
patience  and  perseverance  in  learning  a  number  of 
definitions.  So  viewed,  the  whole  study  lies  in  a 
nutshell ;  apparently  you  ought  to  be  able  to  get  up 
the  science  of  Logic  by  devoting  an  hour  a  day  to  it 
for  perhaps  a  couple  of  months.  And  this  illusion  is 
fostered  by  the  textbooks;  they  are  crowded  with 
detached  definitions  of  technicalities  considered  apart 
from  their  use  in  expressing  doctrines ;  and  the 
doctrines  themselves  are  mostly  not  put  forward  as 
open  to  discussion  or  improvement,  but  claim  to  be 
beyond  all  question  true.  In  fact,  quite  apart  from 
any  desire  to  supply  material  for  the  crammer,  the 
textbooks  generally  assume  that  all  the  doctrines  of 
Logic  may  be  deduced  from  axioms  as  undenial)le  as 
those  of  Euclid,  and  that  unless  this  is  done  the 
'  scientific  foundation  '  is  absent. 

On  the  other  hand,  the  attitude  of  the  interested 
inquirer  is  that  of  the  larger  logical  treatises.  Even 
a  brief  study  of  any  of  these  will  bring  before  us 
forcibly  the  fact  that  Logic  as  viewed  by  them 
resembles  the  natural  sciences  in  being  progressive 
and  full  of  problems  only  partly  solved.  The  more 
we  care  about  the  main  problem  of  Logic,  the  more 
we  find  that  one  question  leads  to  another — one  ques- 
tion requires  the  previous  settlement  of  another — so 
that  the  inquirer's  time  and  trouble  are  spent  for  the 
most  part  not  apparently  or  directly  on  the  main 
problem  itself,^   but  rather  on  its  preliminaries  and 

»  This  may  help  to  explain  Mr.  Bosanquet's  desire  {Essentials  of  Logic, 
p.  2)  to  warn  the  student  against  expecting  Logic  to  have  a  practical  bear- 
ing on  human  life.     See  also  note^  p.  47. 


CH.  i,§3  ^/3f  AND  METHOD  OF  LOGICAL  STUDY  7 

outworks ;  sometimes  on  questions  of  fact  about  the 
nature  of  reasoning  in  general,  or  about  the  connec- 
tion between  thought  and  language,  or  about  the 
nature  of  knowledge  itself;  and  constantly  on  ques- 
tions about  the  meanings  of  the  technical  terms. 
Gradually  we  recognise  that  there  is  no  set  of  posi- 
tive logical  doctrines  which  are  safe  against  every 
kind  of  useful  and  instructive  doubt,  nor  any 
definitions  of  the  technical  terms  which  are  perfectly 
satisfactory  and  final. 

§  3, — The  Assumptions  of  Formal  Logic 

But,  in  the  second  place,  our  quarrel  is  only 
accidentally  with  the  textbooks,— only  so  far  as  they 
keep  alive  the  notion  that  formality  is  the  strength 
of  Logic  instead  of  its  weakness ;  and  there  seems 
to  be  no  good  reason  why  they  should  always  con- 
tinue to  do  so.  Their  treatment  of  Logic  cannot 
deserve  condemnation  merely  because  it  is  elementary, 
nor  merely  because  it  follows  old  tradition ;  it  is 
Formal  Logic,  as  such,  that  calls  for  criticism,  and 
its  venerable  age  is  an  extenuating  circumstance 
rather  than  part  of  the  charge  against  it. 

The  term  Formal  Logic,  as  it  will  here  throughout 
be  used,  does  not  mean  only  the  Logic  that  expressly 
calls  itself  formal,  though  that  is  naturally  the  most 
prominent  type  of  it.  The  open  confession  of  for- 
mality in  Logic  aims  chiefly  at  the  restriction  of  the 
inquiry  to  a  specially  limited  field,  and  for  this 
purpose  certain  assumptions  are  made  which  we  will 
notice  presently.  On  the  other  hand,  the  acceptance 
of  *  formal  truths '  as  satisfactory  —  a  mental  habit 
which  is  encouraged  by  these  assumptions,  but  may 


s 


USE  OF  WORDS  IN  REASONING        part  i 


also  exist  without  them — is  prevalent  eveu  in  systems 
which  do  not  specially  claim  to  be  formal.  It  is 
rather  the  practice  than  the  profession  that  matters. 
We  shall  find  that  (excluding  works  on  purely 
symbolic  Logic)  even  the  most  professedly  formal 
logicians  do  not  succeed  in  reducing  Logic  to  perfect 
formality ;  and  also  that  no  logical  system  can  escape 
formality  altogether.  Our  objections,  therefore,  lie 
only  against  contented  acquiescence  in  certain  prin- 
ciples or  habits  of  thought  which  tend  to  make  the 
science  more  formal  than  it  need  be. 

First,  as  regards  the  restriction  of  the  scope  or 
province  of  Logic.  No  doubt  there  are  some  pur- 
poses for  which  there  must  be  separate  departments 
of  science  or  philosophy,  even  if  they  have  to  be 
separated  in  a  somewhat  arbitrary  way.  The  harm 
arises  only  if  we  keep  to  these  convenient  divisions 
too  rigidly ;  and  that  occurs  whenever  we  forbid 
the  raising  of  a  question,  relevant  to  the  main 
problem  of  the  science,  on  the  ground  that  such 
question  lies  outside  its  scope  or  province.  The  limit- 
ation of  the  scope  of  any  science  is  a  matter  of 
convenience  from  beginning  to  end,  and  any  par- 
ticular limitation  ceases  to  be  convenient  (except  of 
course  to  the  crauimcr)  when  it  is  used  to  block 
inquiry  precisely  at  the  point  where  important  diffi- 
culties have  arisen.  Why  should  we  stop  just  there, 
unless  a  shallow  perfunctory  view  of  the  subject  is 
what  we  are  trying  to  preserve  ?  In  intimate  con- 
nection with  Logic  there  are  other  departments  of 
study,  and  we  starve  Logic  in  so  far  as  we  are  eager 
to  insist  on  their  disconnection  from  it,  —  their 
'otherness.'  For  instance,  the  inquiry  into  the 
value  of  special  modes  of  reasoning  cannot  be  carried 


CH.i,§3  AIM  AND  METHOD  OF  LOGICAL  STUDY  9 

far  without  raising  general  questions  about  the 
reasoning  process ;  and  just  when  a  new  light  is 
beginning  to  break  on  the  subject  we  are  warned 
perhaps  that  the  question  is  psychological,  not  logical. 
Or  something  suggests  a  question  as  to  the  nature 
of  knowledge  in  general,  and  then  we  are  told  that 
the  lof^ician  has  no  business  in  the  domain  of  Meta- 
physics. And  by  carefully  heading  off  inquiry 
wherever  it  threatens  to  become  difficult,  we  may  in  the 
end  so  cramp  the  science  of  Logic  that  it  becomes 
a  mere  collection  of  misleading  formulas,  coupled  or 
not  with  a  little  elementary  Grammar. 

The  extreme  of  this  kind  of  restriction  is  reached, 
naturally,  in  the  deliberate   attempt   to  keep  Logic 
purely  formal.      Those  who  make  this  attempt  explain 
that  when  they  speak  of  a  piece  of  reasoning  as  being 
formally  valid  they  mean  that  its  validity  is  determined 
solely  by  its  form  and  is  in  no  way  dependent  upon  the 
particular  subject-matter  to  which  it  relates.    They  try 
to  retard  ih^process  of  reasoning  as  something  distinct 
from  the  subject-niatter  about  which  it  is  employed, 
and  the  errors  of  reasoning  which  they  intend    to 
contemplate  are  those  only  which  occur  in  the  process 
so  conceived.     The  older  view,   still   held  by  some 
writers,  is  that  the  whole  of  the  department  called 
Inductive  Logic  ^  is  thus  ruled  out.     Whately,  for  in- 
stance, was  openly  scornful  of  its  proposed  inclusion.^ 
But  times  have  changed,  especially  since  the  days  of 
IMill   and  Bain,   and    there    seems  to  be  a  growing 

»  The  distinction  between  deductive  and  inductive  Logic  is  open  to 
criticism  (see  §  62)  ;  but  without  at  present  entering  upon  that,  we  may  say 
that  Inductive  Logic  attempts  to  generalise  about  the  evidentiary  force  of 
facts  obUined  by  observation  and  experiment,  and  to  lay  down  rules  for 
getting  from  such  facts  to  trustworthy  general  knowledge  of  the  course  of 

nature.  ,  .    ^.  .,  r 

2  See  the  Introduction  to  his  La/ic,  and  §  1  of  his  Essay  on  the  province  of 

reasoning. 


10 


USE  OF  WORDS  IN  REASONING        part  i 


.J    V 


tendency  now  ^  to  recognise  Inductive  Logic  also  as 
formal.  At  any  rate  the  usual  treatment  of  that 
subject  is  formal  enough  in  one  main  respect, — that 
it  retains  the  traditional  conception  of  a  reasoning 
process  as  something  separate  from  its  subject-matter, 
and  we  shall  see  how  such  a  conception  sterilises  the 
inquiry  into  the  nature  of  good  and  bad  reasoning. 

When  the  question  is  raised  whether  there  is  any 
such  thing  as  a  process  of  reasoning,  distinct  from  its 
subject-matter,  the  answxr  depends  entirely  on  the 
meaning  we  give  to  the  question.  In  this  respect  it 
resembles  many  minor  perplexities  which  are  more 
familiar ;  for  instance,  the  question  whether  there  is 
such  a  thing  as  Luck.  In  denying  the  existence  of 
Luck,  or  of  a  separate  reasoning  process,  we  need  not 
pretend  that  wx  are  totally  unable  to  understand 
what  excuse  any  one  can  have  had  for  assuming  these 
entities ;  indeed,  until  we  can  see  the  excuse  any 
attempts  to  remedy  the  error  would  have  small  chance 
of  success.  It  is  only  through  finding  the  assumption 
plausible,  and  for  some  purposes  true  and  useful,  that 
we  can  hope  to  find  the  limits  of  its  truth  and  value  ; 
for  it  is  always  among  the  applications  of  a  doctrine, 
not  in  the  doctrine  apart  from  its  applications,  that 
we  must  search  for  its  qualities  and  defects.  To  deny 
the  existence  of  a  separate  reasoning  process  does  not 
necessarily  involve  our  tearing  up  the  old  logical 
system  root  and  branch.  We  have  only  to  graft  a 
modification  upon  it  and  to  cut  away  some  exuberant 
shoots  below  the  ojraft. 

One  elementary  point  to  notice  is  that  when  people 

'  Mr.  Carveth  Read,  in  his  Lcujic,  Dt'dmiive  and  Inductive,  p.  192, 
expressly  says:  "Inductive  Loj^ic  may  be  consideretl  as  having  a  purely 
formal  character."  The  same  desire  is  visible  also  in  his  earlier  book  On  the 
Theory  of  Logic, 


CH.  I,  §3  AIM  AND  METHOD  OF  LOGICAL  STUDY  11 

speak  of  the  validity  of  a  piece  of  reasoning  being 
determined  solely  by  its  form,  they  are  either  not 
speaking  carefully  or  else  are  overlooking  the  fact  that, 
in  order  to  get  assertions  expressed  in  (what  the 
formal  logician  calls)  logical  form,^  it  is  often  necessary 
first  to  consider  their  meaning, — to  consider  what  is 
the  matter  asserted.  Since,  therefore,  in  these  cases 
the  form  is  determined  by  our  view  of  the  matter,  the 
supposed  escape  from  material  considerations  is  to 
that  extent  at  least  illusory. 

But  a  more  thoroughgoing  difficulty  is  to  imagine 
what  can  really  be  meant  by  a  process  of  reasoning 
cut  off  from  that  which  the  reasoning  is  about.  There 
is  a  way,  of  course,  in  which  forms  of  reasoning  may 
be  exhibited  apart  from  special  subject-matter.  We 
may  put  letters  of  the  alphabet  in  place  of  words,  and 
explain  that  these  letters  are  intended  to  have  a 
perfectly  general  meaning,  or  to  leave  blanks  to  be 
filled  in  by  any  words  we  please  ;  we  may  write  down, 
for  instance,  the  argument  "  All  Y  are  Z,  and  all  X 
are  Y  ;  therefore  all  X  are  Z  '* :  or  again,  the  plainly 
inconclusive  argument  *'  All  Z  are  Y,  and  all  X  are 
Y  ;  therefore  all  X  are  Z  "  ; — for  instance,  *'  Birds  have 
wings,  and  so  have  bats ;  therefore  bats  are  birds." 
So  far  no  harm  is  done,  and  there  may  even  be  some 
purposes  for  which  these  and  other  skeleton  forms  of 
reasoning  are  useful.  But  it  is  when  we  take  a 
further  step  that  we  get  into  confusion,  —  when, 
havinor  distinguished  between  forms  which  are  valid 
(t.c.  formally  conclusive)  and  those  which  are  not  so, 
we  seek  to  identify  the  invalid  forms  with  incorrectness 
in  the  *  process  of  reasoning,'  or  the  valid  forms  with  the 
opposite  quality.     The  truth  rather  is,  that  in  the 

>  See  also  §§  30,  57,  and  58. 


12 


USE  OF  WORDS  IN  REASONING        vkwt  i 


first  place  (as  we  shall  presently  see),  where  an 
argument  is  expressed  in  an  invalid  form  the  fault 
cannot  be  satisfactorily  traced  to  the  reasoning  process 
as  distinct  from  the  subject-matter  ;  in  the  second 
place,  that  the  most  effective  kind  of  incorrect 
reasoning  occurs  where  the  mere  form  of  the  ar<T^ument 
is  valid  ;  and  in  the  third  place,  that  whether  it 
happens  to  be  effective  or  not,  its  incorrectness  in 
these  cases  evidently  cannot  be  discovered  by  con- 
sidering the  form  alone. 

There  can  be  invalid  forms,  of  course ;  anybody 
can  write  one  down,  and  if  a  decent  clothing  of  words 
is  found  for  it  a  certain  percentage  of  people  may 
carelessly  pass  it  as  valid.      But,  when  this  happens, 
what  is  the  cause  of  the  error?      To  say  that  the  "" 
reasoning  process  is  incorrec^t  is  merely  a  phrase  which 
declines  to  attempt  any  explanation  ;  for  explanation 
of  an  error  means  the  suggestion  of  a  theory  as  to 
its  causes.     Now   unless  we  are  content  with  some 
such  empty  answer  as  that  ignorance  of  the  rules  is 
the  one  cause  in  all  cases, — an  empty  answer  because 
it  evades  the  question  asked  and  only  tells  us  that 
invalid   conclusions  are  those   which    Formal    Locr'u- 
condemns    by    rule, — it    is    evident  that    the    actual 
causes  of  getting  a  false  conclusion  from  a  pair  of 
premisses  must  be  nearly  as  various  as  the  minds   , 
concerned.     The  persons  concerned  may  or  may  not 
have  heard  of  the  rules,  or  have  tried  to  learn  them, 
and  an  unsuccessful  attempt  to  follow  the  rules  has  a 
different  effect  from  an  attempt  to  reason  directly. 
When    puzzled    students,    presented   with    pairs    of 
premisses   and   asked  to  draw  conclusions,   take   to 
guessing,  their  guesses  are  of  course  determined  some- 
how ;   but    the  varieties   of  such   determination    are 


I 


CH.  I,  §3  AIM  AND  METHOD  OF  LOGICAL  STUDY  13 

beyond  all  counting.  Different  minds  will  retain 
different  scraps  of  the  rules,  and  will  have  undergone 
different  experiences  of  the  success  or  failure  of  pre- 
vious guessing,  and  will  be  affected  differently  by 
mere  jingles  of  sound. ^  But  these  guesses  can  scarcely 
be  called  reasoned  conclusions  at  all ;  at  most  they 
are  reasoned  estimates  of  the  chance  that  a  given 
guess  is  right.  What  is  wanted  rather  is  an  explana- 
tion of  the  case  where  a  person,  wdth  or  without  some 
knowledge  of  the  rules,  thinks  he  sees  that  a  certain 
conclusion  does  legitimately  follow  from  a  given  pair 
of  premisses.  In  such  a  case  can  any  theory  of  the 
cause  of  failure  be  suggested  except  that  the  meaning 
of  one  or  more  of  the  statements  was  wrongly  con- 
ceived,— given  a  wider  extent  of  assertion  than  was  in 
fact  intended  ?  For  however  true  it  may  be  that  all 
Z  are  Y,  if  you  take  it  as  meaning  also  that  all  Y  are 
Z,  you  may  thereby  change  it  from  a  true  assertion 
into  a  false  one ;  and  then  your  mistaken  conclusion 
that  all  X  are  Z  results  from  a  defect  which  is  not  in 
your  reasoning  process  but  in  your  conception  of  the 
subject-matter. 

It  may  be  said  perhaps  that  this  is  a  somewhat 
imaginative  explanation,  since  we  cannot  get  an 
instantaneous  photograph  of  the  mind  in  the  act  of 
reasoning,  but  can  only  give  an  account  of  any  piece 
of  inference  so  far  as  memory  and  imagination  can 
be  trusted  to  reconstruct  the  process  afterwards. 
That  is  quite  true,  but  just  because  the  difficulty  is  a 
real  one  we  have  no  resource  but  to  use  our  imagina- 
tion or  else  give  up  all  attempt  to  explain  the  piece 
of  inference.     The  question  is  whether  definite  fault 

*  See  also  end  of  §  63.  It  is  chiefly  where  reasoning  operations  are  made 
purely  mechanical,  as  in  the  traditional  Logic,  that  jingles  of  sound  are  likely 
to  ape  reasoning. 


^ 


14 


USE  OF  WORDS  IN  REASONING         part  i 


can  1)0  found  with  the  above  account  of  it,  or  a 
better  explanation  suggested.  It  is  not  as  if  there 
were  two  rival  theories  and  we  were  in  doubt  be- 
tween them,  but  our  choice  appears  to  be  between 
this  and  none.  Since  the  conclusion  of  a  valid 
Syllogism  ^  is  contained  in  the  meaning  of  its  pre- 
misses, it  follows  that  to  draw  a  given  conclusion 
from  premisses  which  do  not  contain  it  involves 
some  misinterpretation  of  those  premisses.- 

For  the  purpose  of  showing  how  entirely  the 
phrase  *  incorrect  reasoning  process '  fails  to  account 
for  the  error,  let  us  take  an  example.  It  would 
hardly  be  fair,  perhaps,  to  use  one  of  the  excessively 
obvious  cases  of  inconclusive  reasoning  which  are 
too  often  provided  in  the  textbooks,  and  to  ask 
ourselves  if  we  can  understand  how  it  could  happen. 
For  instance,  the  argument  (given  by  Whately)  that 
"  White  is  a  colour,  and  Black  is  a  colour  ;  therefore 
Black  is  White  "  lacks  realism  too  entirely  to  l)e  a  fair 
example.  We  must  take  one  of  a  kind  that  is  some- 
times met  with  outside  the  exercises  for  students ; 
one  that  might  mislead,  say,  half-a-dozen  voters 
among  a  crowd,  or  an  average  schoolboy.  Any 
plausible  instance  of  what  Formal  Logic  calls  '  un- 
distributed middle ' '  will  serve  very  well  ;  for 
example,  '*  Bad  workmen  complain  of  their  tools ; 
X  complains  of  his  tools,  and  therefore  X  is  a  bad 
workman."  Now  the  question  is,  are  we  to  suppose 
that  the  person  drawing  this  inference  sees  clearly 

*  This  technicality  is  exj)lainetl  in  next  chapter. 

2  One  of  the  commonest  kinds  of  sucli  niiaintcrpretatiou  is  the  tendency 
to  take  'all  Z  are  Y'  as  e<iuivalent  to  'all  V  are  Z,'  but  some  others  are 
noted  at  the  end  of  §  63. 

2  Such  arg\iments  are  always  reducible  to  the  following  type  :  A  case 
(or  set  of  cases)  X,  and  a  class  Z,  agree  in  possessing  the  feature  Y  ;  there- 
fore X  belongs  to  the  class  Z. 


CH.  I,  g  3  AIM  AND  METHOD  OF  LOGICAL  STUDY  15 

the  difference  of  meaning  between  the  statement  that 
l)ad  workmen  complain  of  their  tools,  and  the  state- 
ment that  those  w^ho  complain  of  their  tools  are  bad 
workmen,  and  that  seeing  this  difterence  he  never- 
theless '  reasons  incorrectly '  ;  or  are  we  to  suppose 
that  he  fails  to  see  the  difference  clearly,  and  reasons 
to  his  false  conclusion  '  validly '  from  a  major  pre- 
miss which  is  false  ? 

It  is  fully  admitted  that  no  one  can  do  more  than 
imagine  what  takes  place  in  the  mind  of  the  faulty 
reasoner.  But  why  should  we  do  less  ?  Why  should 
we  assume  that  his  mind  has  acted  in  a  wholly  un- 
intelligible manner  when  we  can  so  easily  make  the 
process  intelligible?  The  second  explanation  above 
su^^ested  refers  us  to  a  cause  which  is  itself  familiar. 
We  all  know  that  assertions  are  frequently  mis- 
understood ;  that  facts  which  are  true  as  they  stand 
expressed  may  be  incorrectly  conceived  by  the 
audience  and  so  falsified.  Every  one  of  us  often  is, 
and  with  very  good  reason,  doubtful  whether  a  given 
sentence  of  the  form  '  All  Z  are  Y '  is  or  is  not  also 
intended  to  cover  the  assertion  that  all  Y  are  Z ; 
there  was  a  time  perhaps  when  we  were  hardly 
awake  to  the  fact  that  there  could  be  any  difference 
of  meaning  between  them.  And  if  we  suppose  this 
common  uncertainty  actually  arising  it  explains  the 
false  conclusion  at  once ;  the  reasoning  was  correct, 
but  one  of  the  statements  was  taken  in  a  sense  which 

made  it  false.  ^ 

The  notion  of  a  process  of  reasoning  which  can  be 

1  Formal  Logic  may  plead  that  by  means  of  its  rule  against  '  simple 
conversion  of  A  '  it  specially  guards  against  this  danger.  That  is  true,  and 
the  rule  is  a  good  one  if  not  teken  as  implying  that  the  form  of  the  sentence 
decides  its  meaning.  But  the  existence  of  the  rule  does  not  alter  the  fact 
that  what  Formal  Logic  would  call  an  invalid  syllogism  may  rather  deserve 
to  be  called  a  valid  syllogism  with  a  fahje  major  premiss. 


16 


USE  OF  WORDS  IX  REASONING         part  i 


faulty  apart  from  mistakes  in  the  siilyect- matter 
l)ecomes  less  and  less  intelligible  the  more  we  inquire 
what  sort  of  existence  it  could  have.  That  the 
process  may  be  spoken  of  *  in  the  al)stract '  ^  is  of 
course  admitted  ;  we  may  speak  of  things  in  the 
abstract  as  much  as  we  please,  at  least  when  any 
clearer  insight  into  facts  is  to  l)e  gained  by  doing  so. 
But  to  ima^nne  that  because  we  can  do  this  therefore 
abstractions  have  independent  existence  is  to  forget 
that  they  are,  after  all,  abstractions.  It  would  be  a 
good  exercise  for  the  student  to  try  to  make  clear  to 
himself  what  a  process  of  reasoning  can  be  when 
entirely  cut  off  from  the  matter  reasoned  about ;  or  a 
process  of  thinking  without  anything  thought  about ; 
or  a  process  of  building,  without  materials  used. 
Whatever  purpose  such  abstractions  may  serve,  the 
one  purpose  they  never  can  serve  is  that  of  throwing 
light  on  the  difference  between  performing  the 
operation  well  and  performing  it  badly ;  for  the 
same  operation  with  different  materials  gives  widely 
different  results. 

But  the  attempt  to  separate  the  reasoning  process 
from  the  subject-matter  is  not  the  only  radical  defect 
of  Formal  Logic.  There  are  also  some  other  half-true 
assumptions  made  by  it,  more  or  less  systematically, 
which  become  untrustworthy  just  at  the  point  where, 
in  applying  logical  doctrines,  doubt  and  difficulty 
and  difference  of  opinion  arise — just  at  the  point, 
therefore,  where  common -sense  views  show  their 
weakness,  and  where  a  more  elaborate  Logic  is 
wanted.  Of  these,  two  w^hich  render  the  technical 
terminology  useless  in  cases  of  doubt  and  difficulty 
are : — 

*  For  a  first  account  of  the  meaning  of  the  word  abstract,  see  §  6. 


CH.  r,  ji  3  AIM  AND  METHOD  OF  LOGICAL  STUDY  17 

The  assumption  that  the  '  logical  character '  of  a 
word,  or  of  an  assertion,  belongs  to  it  quite  in- 
dependently of  its  context ;  and — 

The  assumption  that  a  sentence  which  is  intended 
to  express  an  assertion  is  the  same  thing  as  the 
assertion  which  that  sentence  is  intended  to  express. 

The  first  of  these  requires  to  be  discussed  in 
connection  with  the  technicalities  in  detail,  and  is 
therefore  reserved  for  Part  IIL,  but  the  second 
admits  of  a  little  discussion  here. 

If  failure  to  express  a  clear  meaning  can  ever 
occur, — if  there  can  be  two  different  sentences  ^  ex- 
pressing  the  same  assertion,  or  two  different  assertions 
expressed  in  the  same  form  of  words, — then  it  is 
evident  that  sentence  and  assertion  are  not  the  same 
thing,  and  that  to  use  the  word  *  proposition '  ^  to 
cover  both  is  to  go  out  of  our  way  to  create  per- 
plexities. As  a  help  in  guarding  against  them,  it  is 
better  to  say  *  assertion '  when  we  mean  assertion, 
*  sentence'    when    we    mean    sentence,    and    *pro- 

*  Complete  idpntification  of  sentence  with  assertion  is  not,  so  far  as  I 
know,  oj>enly  and  directly  proi>osed  by  any  logician,  and  probably  could  not 
be  consistently  preserved.  In  fact,  formal  logicians  may  be  found  dis- 
puting among  themselves  whether  '  Victoria  is  the  Queen  of  England '  is 
or  is  not  the  same  assertion  as  'Victoria  is  England's  Queen,'  and  in 
similar  cases  of  slight  verbal  change.  On  the  other  hand,  it  is  notorious  that 
a  creed  may  be  held  in  many  different  senses.  For  some  remarks  on  the 
'immediate  inferences'  of  Formal  Logic,  see  §  64. 

-  The  word   *  proposition '  is  one  of  the  worst  sources  of  confusion  in 
Logic.     Several  of  the  textl)ooks  openly  define  it  as  an  assertive  sentence,  or 
A  sentence  indicative,  and  then  proceed  to  talk  of  propositions  as  having 
certain  relations  to  other  proi^)ositions,— including  or  excluding  them,  for 
instance.      Evidently  they  are  here  speaking  not  of  the  sentence  but  of  the 
meaning  of  the  serilence  (i.e,  the  assertion)  ;  for  the  sentence  'All  X  are  Y  ' 
no  more  includes  the  sentence  '  Some  X  are  Y '  than  the  idea  of  a  spade  can 
dig  the  idea  of  the  ground.     The  relations  which  are  of  interest  to  Logic  are 
l>etween  assertions,   not  between  sentences  ;  any  possible  relations  between 
sentences  are  of  a  wholly  different  order  ;   e.g.    one  may  be  longer  than 
another,  or  more  sonorous,   or  more  grammatical.     It  is  the  assertion,  as 
opposed  to  the  sentence,  which  is  true  if  another  is  true  or  false.     It  is 
only  as  confused  with   the  assertion   that  the  sentence  can  be  viewed   as 
capable  of  truth  or  falsehood.     For  the  relation  between  the  assertion  and 
the  'judgment,'  see  7iot€,  p.  59. 


t 


18  USE  OF  WORDS  IN  REASONING        parti 

position '  only  when  the  context  makes  it  clear  which 
of  the  two  is  meant,  or  when  both  are  meant  indiffer- 
ently.    As  we  shall  have  several  opportunities  of  seeing, 
the  slight  trouble  required  for  avoiding  this  common 
confusTon  is  certain  to  be  a  saving  of  trouble  in  the  end. 
Yet  the  ditference  is  not  always  easy  to  remember. 
There  are  two  chief  sources  of  difficulty  in  holding 
clear  the  distinction  between  assertion  and  sentence. 
The  lesser  of  these   consists   in  our  need  for  using 
concise  ways  of  speech.     We  cannot  be  always  saying 
^'  the  assertion  intended  to  be  expressed  in  the  sentence 
*  All  men  are  mortal '  "  ;  for  convenience  we  say  "  the 
assertion  '  All  men   are  mortal ' "  instead.     But  the 
more  important  of  the  two  difficulties  is  of  another 
kind.     Take    any   case   where  we   recognise   tliat    a 
meaning  expressed   in  words  is  not  quite  what  the 
words  strictly  ought,  or  strictly  profess,  to  mean— for 
instance  a  statement  evidently  too  general,  presumably 
not  insisted  upon  to  the  full  in  our  cooler  moments ; 
like  the  Psalmist's  hasty  assertion  that  all  men  are 
liars.     We  may  soften  it  down  as  much  as  we  please, 
but  nevertheless  the  amended  meaning  itself  can  take 
no  other  form  than  that  of  a  sentence.     By  stating 
the  '  real  meaning '  of  a  sentence  in  other  words  we 
only  raise  up  the  same  difficulty  in   another  shape. 
However   often    the    process    is  repeated  we  cannot 
escape  the  need  of  expressing  the  assertion  in  some 

sentence  or  other. 

The  difficulty,  then,  is  that  the  distinction  between 
assertion  and  sentence  is  clear  only  in  its  *  idea/ 
When  we  ask  for  actual  cases  of  assertion  they  cannot 
be  produced  otherwise  than  in  the  form  of  sentences. 
Hence,  if  we  are  not  careful,  we  get  into  the  habit  of 
simply  identifying  the  assertion  with  the  sentence,  and 


ca  I,  §  4  AIM  AND  METHOD  OF  LOGICAL  STUDY  19 

so  increasing  our  natural  tendency  to  forget  that 
sentences  need  care  in  interpretation.  One  of  the 
greatest  helps  towards  preserving  clear  views  in  Logic 
consists  in  avoiding  the  false  assumption  that  forms 
of  sentence  have  some  peculiar  virtue  which  binds 
assertor  and  audience  equally  to  a  single  indisputable 
meaning.  Any  Logic  which  commits  itself  to  this 
assumption  is  thereby  cut  oft'from  the  hope  of  becoming 
ol  practical  service  in  dealing  with  the  chief  differences 
of  opinion  upon  matters  of  fact ;  for  the  most  effective 
source  of  fallacy  and  dispute  is  always  the  failure  to 
get  our  meanings  clear,  and  the  subtler  the  misinter- 
pretation the  more  effective  it  is. 

But  if  we  resolve  to  think  of  the  assertion  as 
that  wliich  tlie  sentence  attempts  (or  intends)  to 
express,  rather  tlian  as  that  which  the  sentence  does 
express,  we  leave  a  way  open  for  the  effort  to  search 
for  real  meanings  behind  apparent  ones  in  any  actual 
case  that  comes  in  question.  The  point  at  w^iich  to 
stop  asking  for  the  real  meaning  cannot  be  taught  to 
us  by  any  general  rule,  but  at  least  we  may  avoid 
assuming  a  general  rule  to  the  opposite  effect, — a 
downright  prohibition  of  the  most  useful  course  that 
can  be  taken  in  any  inquiry  into  difficult  truth, — on 
the  ground  that  this  is  to  go  outside  Logic.  It  goes 
direct  to  the  centre  of  all  that  Logic  exists  for  the  sake 
of  doing.  The  doctrines  that  it  transcends  are  those 
of  Grammar,  —  generalisations  about  the  forms  of 
speech  which  are  accepted  as  .correct  in  a  given  ao-e 
and  country. 

§  4. — '  Undeniable  Truths  ' 

But  the  harm  of  this  false  assumption  does  not 
end  there.     The  confusion  of  sentence  with  assertion 


20 


USE  OF  WORDS  IN  REASONING 


PART  I 


directly  encourages  one  of  the  most  fatal  defects  of  the 
traditional  system,  namely  its  attempt  to  base  logical 
doctrines  upon  *  undenial)le  truths/  such  as  the  so- 
called  Laws  of  Thought/  Confusion  between  assertion 
and  sentence  tends  to  make  us  think  too  lightly  of 
the  difficulties  of  interpreting  statements  correctly ; 
it  tends  to  prevent  our  seeing  that  an  undeniable 
truth  is,  after  all,  only  expressible  as  a  statement — 
a  sentence — and  that  behind  every  sentence  lies 
the  question  what  precise  interpretation  is  to  be 
put  upon  it.  When  this  is  forgotten  we  slide  easily 
into  the  habit  of  pinning  our  faith  upon  state- 
ments which,  interpreted  in  one  way,  are  rough 
and  misleading  generalisations,  while  interpreted  in 
the  only  possible  other  way  they  are  empty  of  mean- 
ing or  value. 

The  constantly  recurring  difficulty  with  any  general 
truth  is  to  know  exactly  how  to  apply  it,  or  what 
cases  it  covers  and  does  not  cover,  or  how  far  it  pro- 
fesses to  extend.  If  I  assert  that  all  Y  are  Z  (for 
instance,  that  all  excess  of  zeal  is  to  be  avoided)  a 
legitimate  doubt  may  often  be  felt  as  to  the  precise 
range  of  the  assertion  intended,  the  precise  things  or 
actual  cases  which  are  contemplated  under  the  general 
name  Y.  Where  Y  is  a  technical  term  whose  applica- 
tion is  wholly  unknown  to  us,  the  sentence  conveys  of 
course  no  meaning  at  all ;  and  where  we  know  broadly 
the  class  of  cases  intended  by  Y — where  we  can  recog- 
nise the  more  obvious  or  strongly-marked  cases,  but 
are  doubtful  about  the  exact  definition  of  the  class 
— there  a  meaning  is  conveyed,  but  a  meaning 
which  suflers  more  or  less  acutely  from  the  defect 
called  vagueness.     To  this  extent,  at  any  rate,  the 

1  See  §  35. 


CH.  I,  .^  4  AIM  AND  METHOD  OF  LOGICAL  STUDY  21 

meaning  of  any  general   statement  is   the   same  as 
its  application. 

Consider,  for  instance,  a  maxim  which  Jevons  put 
forward  as  of  fundamental  importance  to  Logic, — that 
"  whatever  is  true  of  a  thing  is  true  of  its  like  "—and 
which  he  afterwards  expanded  into  the  statement  that 
**  so  far  as  there  exists  sameness,  identity,  or  likeness, 
w^hat  is  true  of  one  thing  will  be  true  of  another."  ^ 
The  various  alternative  words  used  for  Mike'  show 
that  Jevons  was  to  some  extent  aware  of  difficulties 
of  interpretation  that  might  be  raised,  but  the  really 
fatal  vagueness  of  tlie  maxim  seems  to  have  entirely 
escaped  his  notice.  Does  it  speak  of  things  which 
appear  alike  or  of  things  which  really  are  alike ;  of 
things  which  closely  resemble  or  of  things  which 
essentially  resemble  each  other  ?  Does  it  tell  us  that 
seemingly  sufficient  likeness  is  always  really  sufficient 
likeness  to  warrant  a  particular  inference,  or  does  it 
only  state  that  really  sufficient  likeness  is  really 
sufficient  likeness  ?  We  are  left  to  choose  w^hichever 
of  these  two  opposed  interpretations  we  prefer,  though 
clearly  it  is  only  in  the  latter  interpretation  that  the 
maxim  can  pretend  to  be  an  undeniable  truth. 
Certainly  no  one  would  attempt  to  deny  that  a  true 
analogy  is  a  true  analogy,  or  that  an  essential  resem- 
blance is  an  essential  resemblance,  or  that  if  Wo  things 
or  classes  are  really  {i.e.  sufficiently)  alike  they  really 

^  Subsfitiction  of  Similars,  p.  15.  There  are  also  other  variations  of 
statement  in  his  writings.  E.g.  **  Whatever  is  known  of  a  term  may  be 
stated  of  its  equal  or  e<iuivalent  "  (i6irf.)  ;  "In  whatever  relation  a  thing 
stands  to  a  second  thing,  in  the  same  relation  it  stands  to  the  like  or  equivalent 
oi  thait&QCoiidWimg"  {Principles  of  Sciciwe,  p.  21);  and  "  Whatever  is  true 
of  one  term  is  true  of  any  term  which  is  stated  to  be  the  same  in  meaning 
as  that  term."  This  last  expression  (Privicr  of  Logic,  p.  73)  has  not  the 
vagueness  of  the  others,  but  in  order  to  avoid  evident  absurdity  it  must  be 
taken  as  a  mere  maxim  of  consistency  in  the  use  of  language,  and  as  having 
no  reference  to  the  course  of  Nature. 


I 

I 


22 


USE  OF  WORDS  IX  REASONING         part  i 


are  so.     But  after  all,  the  only  purpose  of  any  general 
rule  is  to  be  applied  in  particular  cases,  and  how  are 
we  ever  to  apply  such  a  rule  as  this?     When  the 
question  is  whether  the  likeness  between  two  given 
cases  is  or  is  not  sufficient  to  warrant  our  inferrin^^ 
about  the  one  case  something  that  we  already  take  to 
be  true  of  the   other,  we  cannot  assume  that  the 
sufficiency  of  the  likeness  is  undeniable ;  or  rather,  it 
is  only  too  easy  to  make  this  assumption,  and  that  is 
the  very  thing  that  Logic  should  guard  us  against 
doing.     In  face  of  the  (juestion  whether  a  supposed 
analogy  is  a  sound  one,  we  can  get  no  help  from  the 
axiom  when  taken  in  the   meaning  which  makes  it 
undeniable ;  and  the  help  we  get  from  it  in  its  other 
meaning  is  delusive.     As  a  rule  of  inference,  therefore, 
it  tells  us  either  a  falseliood  or  nothing.     In  the  former 
interpretation  it  leaves  us  asking  the  very  question  it 
professes  to  answer, — namely,  what  things  are  '  really 
alike,'  or  how  any  proposed  argument  from  analogy 
is  to  be  justified  ;  in  the  latter  interpretation  it  implies 
that  we  can  never  be  deceived  as  to  the  extent  of 
equivalence  between  any  two  things, — that  no  one,  for 
instance,    has   ever   accepted    a    bad    half-crown    by 
mistake.     As  a  general  statement  it  is  only  true  when 
so  interpreted  as  to  leave  its  application  to  actual 
cases  vague   and   dependent   on    further   knowledge 
coming  to  hand.     We  can  never  say,  except  at  a  risk, 
that  two    actual    things   are   '  equivalent,'   and   that 
therefoi-e  something  true  of  the  one  is  true  of  tlie 
other ;  their  equivalence,  in  the  sense  required,  is  only 
proved  after  we  have  discovered  in  some  other  way 
exactly  what  is  true  of  both. 

The  fault  of  this  axiom  is,  then,  that  however 
enlightening  it  may  seem  at  first,  before   its  many 


CH.  I,  §4  AIM  AND  METHOD  OF  LOGICAL  STUDY  23 

exceptions  occur  to  us,  there  soon  comes  a  time  when 
we  begin  to  recognise  some  of  the  ways  in  which  it 
is  misleading, — to  admit  {e.g,)  the  need  of  distinguish- 
ing between  deceptive  and  trustworthy  likeness, 
between  vague  general  likeness  and  likeness  for  a 
particular  purpose,  and  so  on.  Thenceforth  it  is  only 
with  very  large  modifications  that  we  can  accept  so 
loose  a  principle  as  *  Whatever  is  true  of  a  thing  is 
true  of  its  like ' ;  we  want  to  ask  at  once  what  sort 
of  likeness,  or  likeness  in  what  particular  respects,  is  re- 
quired for  true  analogy  in  the  given  case.  Even  if  we 
retain  the  maxim  in  its  original  verbal  form  we  at  least 
add  something  to  our  first  loose  interpretation  of  it. 

It  is  possible  that  some  readers  whose  common 
sense  is  in  a  healthy  condition  will  think  this  point 
unduly  laboured.  The  excuse  is  not  only  that  Jevons 
failed  to  see  it,  even  in  his  large  work  on  the  Prin- 
ciples of  Science,  but  that  the  same  dilemma — 
*' false  or  else  devoid  of  meaning" — vitiates  all  the 
axioms  which  formal  logicians  regard  as  the  rock  on 
which  their  science  is  built,  and  tends  to  vitiate 
some  of  their  less  sweeping  generalisations  also.  A 
further  excuse  is  that,  as  we  shall  see  further  on,^ 
certain  subtler  forms  of  this  vacillation  between  un- 
truth and  truism  are  justifiable,  and  that  therefore 
the  line  between  the  good  and  the  bad  use  of  it  is 
far  from  easy  to  draw ;  so  much  so,  indeed,  that 
both  the  plainest  common  sense  and  the  most  pre- 
tentious philosophy  sometimes  mistake  the  one  for 
the  other.  It  may  therefore  repay  us  to  consider 
the  question  at  some  length,  in  the  hope  of  making 
clear  at  least  some  of  the  reasons  why  Logic  is  so 
prone  to  fall  into  empty  verbiage. 

1  §§  6  and  50. 


24 


USE  OF  WORDS  IN  REASONING        part  i 


1 


A   good   introduction    to   this   ancient   and    far- 
reaching  field  of  controversy  may  ])e  got  by  consider- 
ing first  the  general  aim  of  science  and  the  kind  of 
problem    it    normally   has    to    face.       Though    the 
opposition  between  scientific  and  common  knowledge 
has   enough  reality  and  value   to  ensure  its   being 
exaggerated  in  our  careless  moments,  we  may  take 
for  granted  that  every  one  when  he  thinks  about  the 
matter  will  admit  that  it   is  not  a  thoroughgoing 
opposition.     In  the  first  place,  the  only  conceivable 
r^  aim  of  any  kind  of  knowledge,  whether  common   or 
scientific,  is  the  power  of  dealing  with  concrete  facts 
through  *  wisdom  before  the  event,'  —  the  power  of 
prediction    from   causes   to   effects.      This   does   not 
mean,  of  course,  that  we  can  never  recognise  a  truth 
without  at  the  same  time  having  a  view  of  its  future 
practical   uses,  but   only   that   we   all   instinctively 
assume   that   truth    is   something   which   sooner   or 
later  has  a  practical  value,  even  if  in  a  given  case 
we  may  have  to  wait  an  indefinite  time  before  we 
discover  what  possible  use  the  piece  of  truth  will 
serve.     Theories  —  generalisations  —  are   our   instru- 
ments of  prediction  ;  and  we  all  know  from  experi- 
ence that  apparently  detached  facts,  for  which  no 
immediate  use  can  be   found,  nevertheless  are  con- 
stantly helping  to  mould  our  theories,  and  thus  in 
the  end  aff*ect  our  practice.     So  accustomed  are  we 
to  this  experience  that  we  can  be  quite  content  to 
accept  a  truth    'for  its  own  sake,'  leaving   to   our 
successors  the   task  of  developing   its   applications. 
And  thus,  without  ever  doubting  that  all  truth  is 
ultimately   practical,    we    can    also    appreciate    the 
mathematician's  famous  epigram — "Thank   heaven, 
that  is  a  truth  which  no  one  will  ever  be  able  to 


CH.  I,  §  5  AIM  AND  METHOD  OF  LOGICAL  STUDY  25 

use."  The  question,  which  may  be  verbally  asked, 
what  we  should  do  in  the  case  of  a  statement 
miraculously  known  to  be  both  perfectly  true  and 
perfectly  useless,  is  like  the  question  what  would 
happen  if  a  perfectly  immovable  body  were  to 
encounter  an  absolutely  irresistible  force.  There 
does  not  appear  to  be  any  likelihood  of  the  case 
arising,  since  whatever  miraculous  knowledge  we 
may  possess  never  extends  to  the  possible  future 
uses  of  a  truth  which  now  seems  unpractical  ;  such 
truths  are  merely  stored  away  to  bide  their  time. 

S  5. — IIalf-Truths 

Not  only  are  common  knowledge  and  scientific 
knowledge  alike  in  their  aim,  but  as  a  mere  historical 
fact  the  latter  is  a  development  of  the  former. 
Scientific  knowledge  has  its  roots  in  common  know- 
ledge, and  to  the  end  retains  some  traces  of  its  lowly 
origin.  It  did  not  descend  upon  us  from  heaven 
fully  grown,  but  has  been  evolved  gradually  by  the 
same  process  by  which  our  common  knowledge  ripens 
or  clarifies  itself  even  long  before  it  has  earned  the 
riorht  to  be  called  scientific.  On  this  account  the 
normal  work  of  science  at  any  given  time  is  the 
improvement  of  the  half-truths  that  previous  (or  less 
scientific)  science  has  reached. 

By  a  half-truth  is  not  here  meant  a  statement 
containing  exactly  fifty  per  cent  of  error,  but  a 
statement  (especially  a  generalisation, — a  statement 
of  general  rule)  which  is  only  roughly  true  ;  a  general 
rule  which,  as  interpreted  and  applied,  is  true  in 
some  or  even  in  most  of  its  applications  but  not  in 
all, — no  matter  what  may  be  the  relative  number  of 


s 


26  USE  OF  WORDS  IN  REASONING        parti 

the    true    and    the    fiilse    applications    respectively. 
Such  half-truths — rough  or  approximate  generalisa- 
tions—  are   of  course   exceedingly   common    in    all 
departments  of  knowledge  of  the  way  things  happen, 
whether  called  scientific   knowledge  or  not.      They 
form  in  fact  the  broad  leading  ideas  we  have  about 
the  world  we  live  in,  the  first  vague  conceptions  by 
means  of  which  we  learn  ;  and  the  conflict  between 
those  who  are  content  to   leave  them    uncorrected 
and  those  w4io  wish  to  correct  them  is  everlastino-. 
Outside  science,   common  proverbs  are  perhaps  the 
most   strongly  -  marked    instance   of    the   class.       A 
proverb  is  seldom  or  never  outrageously  false,  and 
yet  it  is  often  no  more  than  a  one-sided  expression 
of  a  truth  which  can  plainly  be  seen  to  have  two 
sides,   or  at  least  to   pass    lightly  over   excei)tions. 
For  example,  the  rule  ''Take  care  of  the  pence  and 
the  pounds  will  take  care  of  themselves"  is  evidently 
not  quite  true  without  exception,  since  another  piece 
of  proverbial  wisdom  reminds  us  that  a  ship  may  be 
lost   through    a    niggardly    use    of   tar.       Or   again, 
*'  Where   there's  a  will  there's  a   way  "   is  not  the 
whole  truth  of  the  matter,  since  a  man   may  have 
the    best   will  in   the   world  to  add  a  cubit  to  his 
stature  and  not  be  able  to  do  it.     And  so  with  most 
of  our  proverbs ;   if  we  take  any   half-truth  as  per- 
fectly true  it  may  l)y  accident  lead  us  either  right 
or  wTong  on  a  given  occasion.     The  theoretical  and 
practical  know  ledge  it  gives  is  the  reverse  of  accurate. 
So  far  as  the  single  occasion  is  concerned,  such  know- 
ledge may  mislead  us,  however  great  its  statistical 
value.      Whether    the  rule   is  extremely  loose,   like 
the  rule  that  a  red  sky  in  the  morning  predicts  a 
storm,  or  nearly  true,  like  the  rule  that  if  you  post  a 


^> 


CH.  I,  §  5  AIM  AND  METHOD  OF  LOGICAL  STUDY  27 

letter  it  w^ill  be  duly  delivered,  its  inaccuracy  may 
be  as  disastrous  to  any  particular  inference  w^e  have 
drawn  from  it.  Even  if  there  be  only  one  unknow^n 
exception  to  a  rule,  the  given  case  may  be  that  one 
exception,  and  there  is  small  consolation  in  the  fact 
that  the  error  was  natural. 

This  kind  of  inaccuracy,  so  obvious  in  the  case  of 
common  proverbs  and  other  rough  rules,  becomes  of 
course  less  easy  to  see  the  higher  we  rise  in  the  scale 
of  careful  or  scientific  generalisation.  And — what  is 
not  so  widely  recognised — it  there  becomes  on  that 
very  account  more  troublesome.  When  the  looseness 
of  a  rule  or  maxim  is  clearly  seen,  its  powder  to  mislead 
is  usually  remembered  and  discounted ;  we  are  then 
content  to  take  it  somew^hat  freely  and  trust  to  a 
vague  and  happy-go-lucky  discretion  to  keep  us  from 
pressing  it  to  unpractical  lengths.  We  retain  the 
verbal  form  of  the  maxim,  but  every  one  puts  his  own 
interpretation  on  it  when  a  question  of  applying  it 
arises ;  experience  teaches  us  that  current  phrases 
often  have  to  be  taken  with  a  grain  of  salt.  And  the 
method  works  ftiirly  well  so  long  as  its  unscientific 
character  is  clearly  recognised,  though  it  sometimes 
causes  friction  where  the  rules  in  question  are  of 
much  importance, — for  instance,  where  they  are  rules 
of  morality  rather  than  of  merely  sensible  conduct. 
The  more  important  it  is  to  have  some  kind  of  definite 
rule  to  follow,  the  greater  becomes  the  temptation  to 
preserve  any  long-established  formula  even  when  the 
contrast  between  what  it  expressly  says  and  what  it 
is  taken  to  mean  has  become  a  source  of  strife  and 
confusion.  Still,  w^e  need  not  question  the  fact  that 
this  way  of  dealing  with  half-truths  has  a  value  in 
some  cases.     Over  a  great  part  of  life — and  especially 


28 


USE  OF  WORDS  IN  REASONING         part  i 


where  action  is  hurried  or  where  (as  in  manners 
and  morals)  several  different  half-truths  compete  for 
acceptance — this  is  often  the  most  convenient  way  of 
letting  our  knowledge  grow.  At  the  cost  of  a  little 
vagueness  we  are  saved  at  least  from  anarchy,  and  it 
is  questionable  whether  in  some  of  these  cases  science 
could  give  us  any  better  results. 

But  it  is  precisely  where  science  has  a  clear  field 
of  action — where  time  is  not  pressing  and  where 
emotion  does  not  greatly  interfere — that  a  different 
treatment  of  half-truths  is  demanded.  From  the 
point  of  view  of  science  the  method  of  free  imaorina- 
tive  interpretation  is  too  unconscious  and  too  ill- 
regulated ;  and  it  fails  to  store  up  the  advances  of 
our  knowledge  in  a  readily  available  form.  So  far  as 
science  can  be  contrasted  with  common  knowledge, 
its  aim  is  to  state  general  rules  so  that  their  correct 
interpretation  shall  not  depend  upon  individual 
genius,  or  upon  skill  and  discretion  in  effecting  happy 
compromises,  but  upon  the  kind  of  care  which  is  open 
to  every  one  to  practise, — care  spent  in  taking  tech- 
nical statements  exactly  in  their  literal  sense.  Science 
therefore  cannot  be  content  with  rules  which  are  stated 
so  as  to  ignore  their  exceptions,  but  it  must  always 
be  trying  to  recognise  the  exceptions  expressly.^  Thus 
the  defects  in  the  statement  of  a  scientific  jreneralisa- 
tion  are  in  two  ways  vitally  important :  on  the  one 
hand  they  are  smaller  defects,  and  therefore  less 
obvious,  and  therefore  more  efiectively  misleading, 
than  those  which  disfigure  the  rules  of  common  sense  ; 
and  on  the  other  hand  science  is  more  interested  in 

*  In  this  connection  it  is  interesting  to  remember  tliat  Darwin  is  said 
(Life,  vol.  i.  i>.  148)  to  have  had  "the  i)ower  of  never  letting  exceptions 
piiss  unnoticed.  Every  one  notices  a  fact  as  an  exception  when  it  is  striking 
or  frequent,  but  he  had  a  special  instinct  for  arresting  an  exception." 


CH.  I,  g  5  AIM  AND  METHOD  OF  LOGICAL  STUDY  29 

getting  its  statements  as  verbally  correct  as  possible. 
That  is  in  fact  the  essential  characteristic  of  its  aim, 
the  characteristic  on  which  its  existence  as  distinct 
from  common  sense  depends.  Its  rules,  like  all  rules, 
are  intended  for  application  in  particular  cases,  but  its 
special  business  is  so  to  state  them  that  they  may  be 
taken  literally,  applied  in  their  whole  extent,  and  still 
found  true. 

The  aim  itself  is  intelligible,  and  well  known. 
But  equally  intelligible,  if  less  familiar,  is  the  fact 
that  scientific  generalisations  normally  do  not  quite 
achieve  it.  Leaving  Mathematics  out  of  account  for 
the  moment,  and  leaving  also  out  of  account  the  few 
cases  where  all  the  world  is  at  present  agreed  in  find- 
ing no  fault  with  a  rule  as  stated,  it  must  be  confessed 
that  the  greater  part  of  what  claims  to  be  scientific 
knowledge  is  in  a  less  unassailable  condition.  Actual 
science  is  mainly  a  battlefield  of  competing  theories 
built  on  a  limited  but  increasing  knowledge  of  facts. 
The  chief  spectacle  presented  by  science  is  that 
of  unfinished  inquiry,  of  unstable  knowledge,  know- 
ledge which  is  nowadays  somewhat  consciously 
unstable.  Whatever  the  ideal  may  be,  the  actual 
work  of  science  mostly  consists  not  in  contemplating 
its  own  perfections  but  in  removing  little  by  little 
its  own  discovered  imperfections;  not  in  deducing 
absolutely  certain  truths  from  undeniable  principles 
but  in  constant  revision  of  both  facts  and  theories  in 
the  eSbrt  to  make  them  harmonise.  And  until  the 
discovery  of  new  facts,  and  of  new  light  on  old  facts, 
comes  to  an  end,  this  growth  and  partial  reorganisa- 
tion of  scientific  knowledge  bids  fair  to  continue. 
Indeed  we  cannot  even  imagine  the  growth  of  know- 
ledge ending  for  lack  of  new  material  to  gather  and 


30  USE  OF  WORDS  IN  REASONING        parti 

of  old  errors  to  correct.  So  far  as  cau  be  seen,  at 
any  conceivable  period  of  the  development  of  human 
knowledge,  our  existing  generalisations  will  be  grosser 
than  the  facts,  and  will  bear  refining  further  when- 
ever the  need  arises.  There  will  thus  always  be  room 
for  the  detection  of  the  untruth  that  remains  embedded 
in  accepted  'truths.' 

So  radical  a  conflict  between  ideal  aim  and  actual 
performance  naturally  leads  to  some  difficult  situa- 
tions. Our  desire  to  make  our  statements  accurate, 
and  the  limitations  of  our  power  of  doing  so,  together 
constitute  a  peculiar  source  of  danger ;  namely  that 
we  shall  be  drawn  into  defending  the  literal  accuracy 
of  a  statement  by  desperate  means,  among  the  easiest 
of  which  is  the  trick  of  turning  it  into  an  undeniable 
truth  by  mere  definition  of  its  terms,  thus  making  it 
beg  the  question  it  professes  to  answer.  Any  state- 
ment, if  it  claims  to  l)e  important,  lends  also  to  claim 
literal  accuracy  ;  and,  as  we  noticed  above,  the  special 
business  of  science  is  to  make  this  claim  more  seriously 
than  it  is  made  in  expressing  our  looser  common 
knowledsre.  On  this  account,  therefore,  science  is 
under  special  temptations  ^  to  force  its  statements  to 
be  true  by  deliberately  making  them  abstract. 


§6. — 'Abstract*  Statkmknts 

The  technical  term  '  abstract '  is  always  contrasted 
with  'concrete,'  but  as  the  latter  word  is  equally 
technical  this  is  only  an  empty  explanation.     A  better 

*  It  is  not  here  meant  that  the  attempt  to  defend  vi'ibal  accuracy  at  all 
costs  is  exclusively  a  scientific  failing.  From  the  Delpliic  oracles  down  to 
the  latest  platitudes  of  j)olitical  controversy,  men  have  always  been  prone  to 
hedge  their  statements  so  that  tlieir  literal  accuracy  should  be  secured.  But 
we  may  here  leave  out  of  account  all  the  meaner  causes  of  the  practice,  such 
as  stupidity,  or  [)ersonal  vanity  and  Rechthaherci.  None  of  these  violent 
explanations  are  needed  in  the  case  of  science,  whether  ancient  or  modem. 


CH.  I,  .§  6  AIM  AND  METHOD  OF  LOGICAL  STUDY  3 1 

short  account  of  it  would  be  that,  as  applied  to  any 
kind  of  knowledge  or  assertion,  'abstract'  means 
vague}  A  general  assertion  suffers  from  abstractness 
in  so  far  as  we  fail  to  see  exactly  how  to  apply  it  in 
concrete  cases.  But  though  this  short  account  is 
true  as  far  as  it  goes,  it  does  not  carry  us  far.  For 
one  thing,  it  seems  to  regard  abstractness  purely  as  an 
evil,  and  does  not  attempt  to  explain  what  justifica- 
tion   there  may  be  for  its  existence  anywhere, a 

question   the  discussion  of  which  belongs  to  a  later 
place  -  in  our  scheme.     At  present  it  may  suffice  to 
notice  that  assertions  which  suffer  to  some  extent 
from  abstractness  are  a  necessary  incident  of  all  pro- 
gress in  knowledge.     At  any  rate  it  is  clear  that,  as 
things  are,  we  are  often  obliged  to  be  content  with 
statements  which  have  some  nucleus  of  truth  in  them 
but  also  a  fringe  of  doubt  and  error ;  w^here  we  are 
only   on    our   way  towards   the   discovery  how   far 
precisely  the  truth  extends.     If  this  slight  taint  of 
abstractness  were  rigidly  ruled  inadmissible— if  the 
process  of  feeling  our  way  towards   a   satisfactory 
generalisation  were  to  be  condemned  altogether— we 
could  never  get  forward  a  step  in  any  concrete  science. 
It  is  only  through  finding  our  generalisations  vague, 
and  then  continually  raising  the  question  w^hat  cases 
precisely  the  general  names  refer  to,  that  our  know- 
ledge of  general  truths  has  any  chance  of  growing. 

But  the  fact  that  a  certain  amount  of  abstractness 
in  generalisations  is  a  necessary  evil,  and  at  the  same 
time  a  necessary  condition  of  intellectual  activity,  is 

*  Of  course  the  word  abstract  does  not  itself  mean  '  vague '  •  rather  it 
means  •  artificially  simplified, '-simplified  by  leaving  certain  consideratiins 
out  of  account,  or  neglecting  a  part  of  a  concrete  whole.  But  abstractness 
of  assertion,  in  so  far  as  it  is  a  defect,  is  the  same  defect  which  is  otherwise 
called  vagueness. 

2  See  pp.  219  fT. 


32 


USE  OF  WORDS  IN  REASONING        part  i 


not  what  specially  concerns  us  here.  For  the  moment, 
what  we  are  considering  is  the  status  of  j^erfecthj 
abstract  truths,  truths  which  are  guarded  against 
criticism  by  being  made  tautological.  Since  every 
half-truth,  as  such,  is  true  in  some  of  its  applications, 
we  can  always  render  it  wholly  true — if  this  kind  of 
*  truth '  is  worth  having — by  restricting  its  meaning  so 
as  to  make  it  refer  to  those  applications  only,  without 
saying  which  they  are.  The  half-truth,  for  example, 
that  likeness  warrants  inference  by  analogy  can  (as 
we  saw  in  §  4)  be  turned  into  an  undeniable  truth  by 
explaining  that  *  likeness '  here  means  only  sufficient 
or  essential  likeness, — an  explanation  which  leaves 
unanswered  the  question  how  to  apply  the  rule  in 
cases  of  likeness  not  yet  known  to  warrant  the 
analogy  in  question.  Such  a  statement  leaves  un- 
answered the  very  question  it  pretends  to  answer. 

And  so  with  all  our  statements  of  *  tendency,'  or 
of  what  would  happen  in  the  absence  of  counteracting 
circumstances.  Either  they  must  be  willing  to  con- 
fess their  applicability  in  the  concrete,  and  thus  to 
stand  some  definite  test,  and  thus  be  open  to  question  ; 
or  else  they  are  nothing  but  a  meaningless  form  of 
words.  For  instance  it  is  undeniable  that  in  the 
absence  of  counteracting  circumstances  every  man 
would  live  for  ever,  but  if  the  general  statement  that 
all  men  are  immortal  were  defended  on  the  ground 
that  it  speaks  only  of  man  in  the  abstract, — man 
considered  apart  from  the  counteracting  circumstances 
which  in  fiict  surround  him, — how  could  such  a 
statement  be  either  applied  or  tested?  Similarly, 
water  in  the  abstract  (H2O)  is  undeniably  pure  water, 
and  yet  the  statement  that  all  water  is  pure  would 
be  either  false  or  meaningless.     In  examples  of  this 


CH.  r,  ^  6  AIM  AND  METHOD  OF  LOGICAL  STUDY  33 

kind,  no  doubt  the  absurdity  of  the  defence  is  evident, 
but  it  naturally  becomes  less  so  where  the  half-truth 
defended  is  more  nearly  true.^ 

The  emptiness  of  purely  abstract  truths  is  hidden 
from  us  mainly  by  our  bad  logical  habits,  among 
which  two  are  chiefly  to  blame,— the  confusion  between 
assertion  and  sentence '  already  mentioned,  and  the 
inclination  to  take  Mathematics  as  the  type  of  science 
in  general.     In  Geometry,  for  instance,  as  every  one 
knows,   we   have   statements  which    are   apparently 
quite  abstract  and  yet  are  as  full  of  meaning  as  any 
assertion  can  be.     A  point  or  a  line  is  defined  so  as 
to  preclude  the  possibility  of  there  being  any  such 
thing   in   the  concrete  world.      No  visible  point  is 
small  enough  to  satisfy  the  definition,  and  none  would 
be  small  enough  even  if  our  visual  power  were  in- 
creased to  any  specified  extent.     And  the  same  with 
the  breadth,  or  with  the  straightness,  of  a  line.     So 
that  when  it  is  said  that  any  two  sides  of  a  triangle 
arc  together  greater  than  the  third  side,  or  that  a 
bent  line  is  longer  than  a  straight  line  between  the 
same   two   points,   the   assertion,  strictly   taken,   is 
perfectly  abstract. 

But,  ixs  a  matter  of  fact,  are  geometrical  axioms 
ever  quite  strictly  taken  ?  At  any  rate  it  is  clear 
that  wherever  they  are  applied  the  strict  interpreta- 
tion of  them  would  be  irrelevant.  Just  because  any 
actual  lines  and  angles  are  not  the  ideal  thing  but 
only  an  approximation  to  it,  therefore  the  principles 
l>y  which  we  judge  of  their  quantitative  relations  to 
each  other  must  either  speak  of  approximations  or 

iioucea  by  Mr.  Knox  in  Mind  for  January  1900. 

assertion  ft  t  '"f  "^^^^^  ^^  ,^unie  that  if  a  sentence  has  the  form  of  an 
assertion  it  must  also  have  the  reality.     And  see  further  p.  36  below. 

3 


34 


USE  OF  WORDS  IN  liEASONIXG        part  i 


else  be  irrelevant.  The  applicable  meaning  of  these 
axioms  lies  therefore  not  in  their  strictlv  a})stract 
interpretation  but  in  something  else  ;  their  iunction 
as  rules  of  inference  depends  on  the  fact  that  they 
hold  true  when  interpreted  as  comparative  statements 
about  concrete  cases.  Any  statement,  for  instance, 
about  the  properties  of  a  straight  line  or  a  circle 
would  be  devoid  of  application  if  it  could  only  l>e 
applied  to  these  unrealised  perfections  ;  but  it  happens 
to  be  also  proportionately  applicable  to  actual  lines 
or  figures  in  so  far  as  they  approach  straightness  or 
circularity.  The  rule  that  a  straight  line  is  the 
shortest  distance  between  two  points  need  not  be 
taken  as  saying  anything  more  than  that  of  any  two 
lines  drawn  between  two  points  the  one  which  is 
straighter  will  also  be  shorter.  It  is  in  this  sense 
that  we  apply  it  whenever  we  take  a  short  cut  across 
a  corner.  In  the  same  wav  the  axiom  that  thin^'-s 
which  are  equal  to  the  same  tiling  are  equal  to  one 
another  may  be  applied  to  approximately  equal  thin^^s 
by  comparison  with  others  which  are  further  removed 
from  equality.  That  fact,  and  not  the  purely  abstract 
truth,  is  the  justification  for  our  common  rou<Th  use 
of  any  weights  or  measures. 

Turning,  however,  from  statements  of  quantity  to 
those  of  quality,  we  find  on  the  whole  tliat  this  way 
of  interpreting  a  purely  abstract  statement  cannot 
be  employed  except  at  great  risk.  Quality  differs 
from  quantity  in  the  fact  that  simple  measurement 
applied  to  it  can  only  help  us  quite  irregularly  and 
uncertainly  in  predicting  comparative  effects.  This 
holds  good  to  some  extent  even  of  well-known  and 
easily-tested  qualities  like  heat  and  cold,  but  much 
more  so  when  the  qualities  in  question  are — as  most 


ciL  I,  ^  C  AIM  AM)  METHOD  OF  LOGICAL  STUDY  35 

qualities  are— of  a  vaguer  or  more  complicated  kind. 
Compare,  for  instance,  Jevons'  axiom  about  likeness 
with  the  one  just  quoted  about  equality.  The  state- 
ment that  wliatever  is  true  of  a  thing  is  true  of  its 
like  cannot  be  safely  applied  to  cases  of  approximate 
likeness;  a  detected  false  coin,  liowever  nearly  it 
resembles  a  real  one,  is  totally  condemned.  Likeness 
is  a  (juality  which  does  not  admit  of  simple  numerical 
measurement,  since  likeness  or  unlikeness  in  one 
small  detail  may  for  a  given  purpose  outwei^^h  un- 
ikenoss  or  likeness  in  any  number  of  others.  The 
never-ending  problem  of  qualitative  science  is  to  find 
out  more  completely  what  is  the  precise  importance 
of  this  or  that  point  of  likeness  or  unlikeness  between 
any  two  things  or  events.  To  count  them  all  equal 
for  every  purpose— to  adopt  the  principle  '  One  point 
of  likeness,  one  vote  '—is  to  be  as  unscientific  as 
possil)le. 

Here   then   is  at  least  one  reason  why  it  will  not 
<lo  to  take  Mathematics  as  the   type  of  science  in 
general.     By  so   doing   we   obscure   the   distinction 
between    generalisations   which,  interpreted  as  com- 
parative, can  be  trusted  without  reserve,  and  those 
which  are  merely  working  hypotheses  or  half-truths, 
demanding  continual  improvement  through  their  ap- 
plication in  concrete  cases  in  order  to  note  exceptions 
earefully.     The  attempt  to  make  such  generalisations 
undeniable  by  definition   is  an   attempt  to  end  by 
main   force  the  wholesome  and  instructive    conflict 
between  tlieory  and  fact,  through  which  all  our  know- 
ledge of  Nature  has  grown  and  is  growing ;  and  its 
result  is  to  give  us  formulas  which,  interpreted  in  one 
sense,  are  half-truths  uncriticised,  while,  interpreted 
so  as  to  guard  them  against  all  criticism,  they  are 


36 


USE  OF  WORDS  IN  REASONING        part  i 


Pi 


I 


1 


meaningless  ;  formulas  which  produce  a  false  security 
and  serve  as  a  mental  narcotic.     Of  course   if   we 
could  remember  consistently  that  they  are  abstract 
then  there  would  be  no  harm  in  them,  as  well  as  no 
good.      But   we    cannot    consistently   preserve   this 
attitude  towards  a  general    statement.     We  cannot 
help  assuming  that  a  general  rule  is  something  which 
has  to  be  applied  in  particular  cases,   even  though 
when   hard  pressed  to  defend  its  accuracy   we  seek 
the  spurious   safety    of    an    abstract    interpretation. 
Thus  Mr.  Bradley's  well-intentioned  remark  that  ''  we 
never  at  any  time  wish  to  use  tautologies  "  *  needs 
some  expansion.     It  is  true  perhaps  that  we  do  not 
love  tautology  for  its  own  sake,  but  as  a  means  to  an 
end  some  of  us  are  only  too  ready  to  use  it  on  occa- 
sion.    The  purely  abstract  interpretation  of  a  general 
statement  is  usually  an  afterthought.     It  is  when  we 
find  a  maxim  false  in  its  obvious  interpretation,  and 
are  afraid  to  admit  its  falsity,  that  we  take  refuge  in 
the  interpretation  that  makes  it  true  but  futile.     It 
is  in  the  eftbrt  to  evade  criticism  that   the  meaning 
of  the  maxim  is  limited  until  it  reaches  the  vanishing- 
point  and  thus  ceases  to  be  an  assertion. 

And  the  confusion  of  assertion  with  sentence 
naturally  helps  to  support  this  shifty  practice.  The 
hal)it  of  taking  the  sentence  as  being  the  assertion, 
instead  of  as  being  merely  the  outer  shell  or  husk  of 
it, — merely  that  through  which  the  assertion  is  more 
or  less  doubtfully  revealed, — must  tend  to  make  us 
assume  that  a  sentence  which  looks  assertive  really 
is  so.  No  doubt  the  identification  of  sentence  with 
assertion  is  never  carried  quite  to  the  extreme ;  every 
one  would  allow  that  two  distinct   sentences    may 

*  Principles  of  Logic,  p.  131.     See  also  Mind,  1894,  p.  340. 


I 


CH.  I,  §  6  AIM  AND  METHOD  OF  LOGICAL  STUDY  37 

express  the  same  assertion,  and  no  one  would  claim 
that  the  sentence  {e.<j.)  *  Nothing  exists'  has  any 
meaning.  But  it  does  interfere  with  our  seeing  that 
where  we  take  a  sentence  which  expresses  a  general 
assertion  only  partly  true,  and  then  in  order  to 
escape  criticism  so  define  its  terms  as  to  make  its 
denial  nonsensical,  the  assertion  is  lost  and  only  the 
sentence  remains.  The  sentence  *  All  Y  are  Z '  {e.cf, 
*  Luxury  is  to  be  condemned')  gets  what  assertive 
force  it  has  from  our  power  of  recognising  this,  that, 
and  the  other  case  as  Y  {e.g.  this  or  that  expense  as 
luxurious).  But  if  in  answer  to  the  question  what 
Y  means  in  this  sentence  we  can  only  say  that  we 
mean  by  it  those  cases  of  apparent  Y  which  really 
are  Z,  then  by  that  act  of  definition  we  have  deprived 
the  sentence  of  every  shred  of  its  assertive  meaning, 
and  turned  it  into  a  postulate  about  the  word  Y. 
Yet  the  sentence  is  there  unharmed,  and  the  more 
we  tend  to  confuse  sentence  with  assertion  the  less 
can  we  see  that  the  assertion  has  disappeared.  The 
consequence  is  that  the  exceptions  to  the  half-truth 
that  *  All  Y  are  Z '  tend  to  remain  unnoticed ;  our 
knowledge  of  the  extent  to  which  that  generalisation 
may  be  trusted  cannot  progress ;  and  in  our  anxiety 
to  get  certainty  in  place  of  half-truth — and  to  get  it 
as  simply  and  cheaply  as  possible — we  have  palmed 
off  upon  ourselves  a  sham  assertion. 

The  attempt  to  use  this  kind  of  refuge  against 
criticism  is  not,  of  course,  always  made  openly  and 
definitely.  The  commoner  forms  of  it  are  subtler  and 
less  extreme.  They  are  often  to  be  met  with  in  long- 
established  fields  of  controversy,  for  example  where 
difference  of  opinion  exists  about  religion  or  politics 
or  conduct.    Whenever  (e.gr.)  we  find  a  particular  form 


iti< 


i 


38 


USE  OF  WORDS  IN  REASONING        part  i 


of  reliijiori  defeixled  on  the  'auund  that  '  irreli^ioii 
US  fatal ;  or  a  })olitical  party  defended  on  the  ground 
that  some  abstract  virtue,  such  as  order  or  progress, 
is  valual)le  ;  or  a  phrase  like  '*  all  property  is  theft" 
defended  on  the  ground  that  the  existing  industrial 
system  is  in  some  respects  unfair  to  the  proletariat ; 
or  a  particular  line  of  conduct  condemned  on   the 
ground  that  '*  we  ought  not  to  do  evil  that  good  may 
come,"  or  defended  on  tlie  ground  that  "  a  man  must 
act  according  to  his  liorhts "  ;    in  all   such  cases  we 
have  an  opportunity  of  o])serving  a   half-truth  pre- 
paring to  take  refuge  in  this  manner  from  the  critical 
attack.       The    purpose,    however    instinc^tive,    is    to 
entice  the  critic's  attention  away  from  the  (juestion 
whether  these  vague  general  truths  are  here  (tpplied 
correctly,  and  to  pretend  that  their  tinith  is  in  dis- 
pute.    Not  only   proverl)S,  hut  accepted  verbal  for- 
mulas of  any  sort  have  an  a})pli(*able  meaning  which 
is  partly  true  and  partly  false.     No  one  of  them  is 
raised  above  all  danger  of  misa{)i)lication.     It  is  ditti- 
eult,  no  doul)t,  to  see  our  own  religious  or  political 
creed  as  a  mere  half-truth,  but  not  impossible  if  we 
think  of  the  majority  of  those  who  honestly  profess 
to  hold  it.     Any  creed,  taken  in  some  sense  in  which 
it  is  not  understood  by  its  adherents  may,  of  course, 
be  the  perfection  of  wisdom ;  but  taken  as  it  is  in 
practice    understood  it  is   always    imperfectly   true. 
And  so  far  as  we  succeed  in  hiding  its  imperfections 
by  mere   abstract  definition,  it  is  as  if  we  were  to 
argue  that  Thames  water  is  pure   because   water  is 
nothing  but  H.jO,  or  because  all  water  is  pure  in  the 
absence  of  counteracting  circumstances.      Of  course 
pure  water  is  pure  water,  and  virtue  is  virtue,  and 
true  analogy   is  true   analogy.      But   how  do  these 


(  n.  I,  .^  7  AIM  AND  METHOD  OF  LOGICAL  STUDY  39 

statements  bear  upon  any  questions  that  can  be  at 
issue  ?  When  recognised  as  truisms  they  are  wholly 
inoperative;  when  confused  with  doctrines  their 
effect  is  to  hide  from  us  the  imperfections  of  our 
actual  doctrine,  and  so  to  check  the  gradual  develop- 
ment of  loose  half-truths  into  something  better.  The 
defender,  let  us  grant,  wants  to  preserve  the  formula 
intact  for  the  sake  of  the  truth  that  is  in  it.  But 
to  preserve  it  quite  intact,  in  its  applicable  meaning, 
is  beyond  the  powder  of  any  one  in  face  of  criticism. 
So  he  gives  it  an  inapplicable  meaning,  for  a  refuge 
in  times  of  attack.  The  trick  is  too  often  effective. 
In  the  general  ignorance  of  Logic  which  prevails,  and 
which  is  fostered  by  the  traditional  teaching  system, 
it  is  not  difficult  to  make  people  accept  a  circular 
truism  as  a  deep  philosophical  truth. 

S  7. — The  Purpose  of  Technical  Terms 

In  addition  to  the  slippery  or  ghost-like  nature 
of  undeniable  truths,  there  is  a  further  reason  why 
the  notion  of  progress  suits  Logic  better  than  the 
notion  of  perfect  axiomatic  certainty ;  namely  the 
fact  that  while  a  mathematical  doctrine,  once  appre- 
hended, is  never  afterwards  found  misleading,  exactly 
the  reverse  is  the  case  with  our  logical  doctrines. 
When  knowledge  of  Logic  is  identified  with  know- 
ledge of  the  difference  between  good  and  bad  reason- 
ing, it  is  evident  that  any  person's  logical  training  is 
a  gradual  growth,  the  beginnings  of  which  are  lost  in 
the  mists  of  memory.  Our  recognition  of  the  truths 
(or  supposed  truths)  of  Logic  does  not  begin  only 
when  we  begin  to  study  the  books,  or  attempt  to 
express  the  truths  in  technical  language.  Just  as  we 
form  a  vague  notion  of  the  nature  and  aim  of  Logic 


40 


USE  OF  WORDS  IN  REASONING         part  i 


long  before  we  care  to  inquire  closely  into  its  details, 
so  our  notion  of  the  difference  between  good  and 
bad  reasoning  is  gathered  at  first  in  an  irregular 
accidental  manner,  and  grows  clearer  and  fuller  with 
the  growth  of  our  experience  of  reasoned  beliefs  and 
their  value.  A  Logic  of  some  sort  every  one  has,  if 
only  a  few  vague  ideas  more  or  less  relevant  to  the 
main  problem.  At  a  very  early  age  the  ordinary 
child, ^  among  civilised  nations,  makes  some  acquaint- 
ance with  the  misleading  or  puzzling  power  of  lan- 
guage, and  so  begins  to  reflect  in  a  desultory  manner 
upon  the  tricks  that  words  are  apt  to  play  upon  our 
thought ;  and  probably  every  such  child  by  the  time 
he  is  ten  years  old  has  already  acquired  a  scrappy 
collection  of  logical  half-truths  which  influence  his 
judgment.  As  we  grow  older  we  modify  these  and 
extend  them,  but  as  far  back  as  we  can  remember  we 
have  always  had  some  views,  of  a  sort,  about  the 
snares  of  reasoning.  It  is  not  the  facts  of  reasoning 
which  are  recondite,  but  rather  the  truth  about  those 
facts, — the  subtle  analogies  between  facts  that  seem 
different  and  the  subtle  diflerences  between  facts  that 
seem  alike.  In  some  other  sciences  the  facts  are  often 
hard  to  come  at,  and  any  new  discovery  may  bring 
much  illumination  with  it.  But  in  Logic  almost 
every  fact  is  trite  and  familiar,  and  the  illumination 
of  them  is  the  difficult  work  required.     For  instance, 

^  In  a  chapter  entitled  "The  Little  Linguist,"  in  Prof.  Sully's  Studies 
of  Childhood,  some  interesting  instances  are  given,  one  of  the  children 
being  only  about  two  and  a  half  years  old,  and  others  above  four  and  five. 
The  author  remarks,  "There  is  nothing  more  instructive  in  this  connection 
than  the  talk  of  children  themselves  about  words.  They  build  up  quaint 
speculations  about  meanings,  and  try  their  hand  bravely  at  definitions.  .  .  . 
There  is  something  of  this  same  desire  to  get  bohind  words  in  children's 
word-play,  as  we  call  it,  their  discovery  of  odd  affinities  in  verbal  sounds, 
and  their  punning.  Though  no  doubt  this  contains  a  genuine  element  of 
childish  fun,  it  betokens  a  more  serious  trait  also,  an  interest  in  word-sounds 
as  such,  and  a  curiosity  about  their  origin  and  }»urpose." 


CH.  I,  §  7  AIM  AND  METHOD  OF  LOGICAL  STUDY  41 

one  of  the  commonest  problems  for  the  logician  is  to 
take  a  couple  of  apparently  contradictory  logical 
doctrines  ^  each  of  which  appeals  to  us  as  true,  and 
to  place  them  in  some  light  which  shall  remove  the 
contradiction.  In  the  less  perplexed  and  less  careful 
mind  of  the  common-sense  reasoner  these  truths — 
like  pairs  of  conflicting  proverbs — may  lie  comfortably 
side  by  side ;  but  the  logician  is  specially  under 
obligations  first  to  see  and  then  to  reconcile  the 
contradictions.  For  him  there  is  less  chance  of  easy 
contentment  with  truths  which  stultify  each  other. 

Thus  we  are  never  quite  without  logical  doctrines, 
but  we  begin  with  vague  and  confused  ones  and 
gradually  make  them  less  vague,  gradually  find  out 
how  through  their  vagueness  they  become  misleading 
when  applied  to  actual  pieces  of  argument.  After 
the  very  first  steps  are  taken,  therefore, — at  a  date 
to  which  our  memories  will  not  carry  us  back, — to 
learn  the  truths  of  Logic  is  always  to  correct  some 
that  were  held  before ;  to  modify  over-simple  rules 
so  as  to  allow  for  their  exceptions.  Therefore  our 
logical  education  consists  from  first  to  last  in  the 
attempt  to  rectify  half-truths,  to  express  them  with 
precision ;  and  since  this  is  an  endless  problem  our 
knowledge  of  the  technicalities  also — the  instruments 
of  precise  expression — must  be  progressive  rather  than 
final. 

Technical  terms,  as  we  all  know,  require  to  have 
their  meaning  carefully  fixed,  and  this  is  done  by 
means  of  what  everybody  calls  definition.  On  the 
other  hand  many  people  have  not  clearly  recognised 
the  fact  that  it  is  only  in  the  attempt  to  become 


*  E.g.  the  doctrine  that  ambiguity  absolutely  destroys  meaning,  and  the 
doctrine  that  a  small  amount  of  ambiguity  is  harmless.     See  chap.  vii. 


42 


USE  OF  WORDS  IN  REASONING         part  i 


accurate  that  our  statements  have  any  need  to  become 
technical ;  or  that  technical  terms  exist  only  for  the 
purpose  of  expressing  doctrines  precisely,  and  are  not 
in  themselves  or  apart  from  this  purpose  things  with 
a  value.  The  textl)ooks,  for  reasons  noticed  ahove, 
encourage  the  view  that  definitions  of  the  technical 
terms  are  to  be  learnt  as  isolated  facts  preliminary  to 
the  rest  of  the  science,  just  as  Euclid's  definitions  may 
be  learnt  once  for  all.  But  this  plan  helps  to  obscure 
the  fact  that  when  you  have  so  learnt  them  you  are 
only  at  the  beginning  of  the  difficulty  which  is  always 
troubling  Logic,  and  which  never  troubles  Geometry, — 
the  difficulty  of  using  your  definition  to  tell  you 
precisely  how  some  doctrine  sliall  be  interpreted  in 
particular  cases.  It  thus  tends  to  prevent  our  seeing 
that  an  extension  of  our  knowledge  of  particular  cases 
is  always  liable  to  modify  the  definitions  with  which 
we  had  previously  been  contented.  The  traditional 
view  of  the  matter — the  view  adopted  in  the  text- 
books— is  based  upon  our  loose  popular  notions  of  the 
nature  and  use  of  definition,  notions  which  confuse 
under  that  name  many  different  operations.  As  a 
matter  of  fact  there  are  several  purposes  of  definition, 
several  diiferent  reasons  why  we  may  want  a  word's 
meaning  stated ;  and  among  these  a  broad  division 
into  two  main  kinds  should  always  be  kept  in  view. 
Sometimes  in  asking  for  a  definition  we  want  to 
know  in  general  what  is  the  meaning  of  a  word,  how 
it  is  used  or  how  it  ought  to  be  used  in  most  of  its 
possible  contexts, — for  instance,  what  is  the  most 
widely  accepted  meaning,  or  the  most  convenient 
meaning  for  general  purposes,  or  the  meaning  ac- 
cepted by  the  best  authorities,  or  the  meaning  most 
historically   accurate,   most   prominent   at  the   time 


I 


v\\.  \,^1  AIM  AND  METHOD  OF  LOGICAL  STUDY  4:3 

when  the  word  was  first  invented  or  adopted.  Some- 
times, on  the  other  hand,  none  of  these  questions  are 
asked,  but  the  questioner's  whole  desire  is  to  dis- 
cover how  the  word  is  used  in  some  assertion  where 
he  finds  it  ambiguous,  and  so  to  get  the  ambiguity 
removed.  Both  these  processes  are  commonly  called 
definition,  and  the  information  we  get  in  answer  to 
either  kind  of  question  has  a  certain  value.  But 
there  is  a  real  difficulty  in  remembering — what  is 
evident  enough  when  we  think  about  it — that  an 
answer  which  is  valuable  for  the  former  purpose  may 
have  (on  a  particular  occasion)  not  the  smallest  value 
for  the  latter.  The  *  general'  definition  may  give 
you  no  hint  as  to  the  way  in  which  a  particular 
assertion  is  meant  to  be  interpreted.  You  may 
know  the  general  meaning  of  a  word  and  still  find 
it  ambiguous  in  a  particular  context,  and  then  of 
course  the  best  possible  definition  of  the  former  kind 
may  only  give  you  stale  information  and  do  nothing 
towards  removing  your  difficulty. 

For  example,  take  the  statement  that  explosive 
bullets  are  forbidden  in  civilised  warfare.  About  the 
general  meaning  of  the  w^ord  *  explosive '  there  is 
not  much  doubt  or  difficulty;  and  the  rule  against 
tlie  use  of  such  bullets  is  therefore  fairly  well  under- 
stood. But  now  imaorine  that  a  doubt  has  arisen 
whether  some  new  kind  of  expanding  bullet  comes 
under  the  term  *  explosive '  as  here  intended  ;  then  our 
knowledge  of  the  meaning  of  the  rule  is  destroyed  so 
far  as  that  particular  case  is  concerned,  as  long  as  the 
doubt  continues.  Here  is  a  new  invention  which 
acts  in  somewhat  the  same  way  as  an  explosive 
bullet  of  the  more  undenial»le  kind,  and  yet  differs 
from  it  in  certain  respects.     Is  the  resemblance  im- 


44 


USE  OF  WOllDS  IN  REASONING         part  i 


portant  enough  to  make  us  class  this  kind  of  bullet 
as  explosive,  and  so  enlarge  the  old  meaning  of  that 
term  as  here  employed ;  or  is  the  difference  so  im- 
portant that  the  resemblance  need  not  count?  In 
questions  of  this  kind  we  often  find  opinion  strongly 
divided — more  persistently,  perhaps,  than  anywhere 
else.  We  think  we  have  a  clear  idea  of  the  meaning 
of  a  given  word,  and  then  some  day  our  knowledge  of 
particular  cases  is  enlarged  and  we  find  the  meaning 
not  so  clear  as  we  thought.  The  consequence  is 
that  w^e  fail  to  understand  clearly  some  assertion  in 
which  the  w^ord  occurs.  A  new  invention,  or  a  new 
discovery  of  fact,  cannot  avoid  raising  some  per- 
plexities of  this  kind,  and  as  long  as  novelty  is  to  be 
expected  in  the  facts  we  have  to  name,  our  existing 
definitions  will  be  unstable.  Wherever  progress  of 
knowledge  is  possible  our  definitions  are  liable  to 
revision  and  change.  The  first  European  who  dis- 
covered a  black  swan  was  placed  in  this  dilemma. 

New  inventions  or  discoveries  are,  however,  not 
the  only  ways  in  which  knowledge  may  grow,  and 
they  have  specially  little  to  do  with  the  growth  of 
our  knowledge  of  Logic.  That,  as  we  have  just 
noticed  (p.  40),  consists  scarcely  at  all  in  the  finding 
of  new  facts  hitherto  inaccessible,  like  the  black 
swans  of  Australia  or  the  irrioration  works  on  Mars, 
but  in  achieving  a  more  and  more  precise  expression 
of  general  truths  which  are  in  a  sense  familiar  and 
yet  are  too  loosely  conceived, — general  truths,  too, 
the  whole  purpose  of  which  is  to  be  applied  in 
particular  cases,  and  which  apart  from  such  applica- 
tion would  have  no  meaning.  The  technicalities  of 
Logic  are  needed  to  express  the  doctrines  of  Logic, 
and  the  definitions  are  needed  in  order  that  we  may 


'4 


CH.  i,S7  AIM  AND  METHOD  OF  LOGICAL  STUDY  45 

understand  the  doctrines  enough  to  apply  them  even 
in  difficult  cases,  and  so  to  recognise  any  exceptions 
there  may  be.  In  settling,  either  way,  the  question 
of  definition  we  at  the  same  time  increase  our  know- 
ledge of  the  rulers  limit  of  value  in  application. 

From  the  inquirer's  point  of  view,  then,  the 
object  of  studying  the  technicalities  of  Logic  is  not 
merely  to  make  some  acquaintance  wdth  the  formulas 
and  definitions  that  are  w^idely  accepted,  or  that  have 
been  invented  or  defended  by  this  or  that  writer,  or 
school  of  philosophy.  So  far  as  any  such  object 
remains  in  view  at  all,  it  becomes  of  secondary  im- 
portance, and  our  primary  aim  is  to  study  the 
technicalities  in  relation  to  the  truths  they  can  be 
used  to  express.  These  truths  (or  half-truths)  them- 
selves are  the  real  centre  of  logical  interest,  and  the 
technical  terms  are  only  the  machinery  proposed  for 
expressing  them  with  the  greatest  attainable  precision, 
— machinery  which  is  itself  open  to  improvement  and 
therefore  open  to  criticism  in  its  details.  Where  a 
doctrine,  confronted  wuth  a  doubtful  case,  is  found  to 
lack  precision,  we  have  our  choice  between  two 
courses, — to  amend  the  doctrine  by  noticing  the  case 
as  an  exception,  or  to  amend  the  definition  so  as 
to  make  it  include  the  case.  Just  as  the  rule 
that  explosive  bullets  are  forbidden  may  work  quite 
smoothly  till  a  new  kind  of  bullet  comes  in  question, 
and  then  calls  for  amendment  in  one  of  these  two 
ways,  so  with  every  generalisation  of  Logic.  To 
make  a  step  forward  is  always  to  find  ourselves 
called  upon  to  decide  whether  we  shall  amend  a 
previously  accepted  rule  by  registering  an  exception, 
or  on  the  other  hand  amend  a  previously  accepted 
definition  by  extending   it.     Whichever   course   we 


46 


USE  OF  WORDS  IN  REASONING        i-aut  i 


adopt  we  make  the  rule  less  vague ;  we  gain  an 
increased  understanding  of  its  precise  meaning  and 
value. 

It  is  of  course  only  in  the  attempt  to  make  our 
loijical  views  more  and  more  scientific  that  we  jret 
drawn  into  these  questions  about  the  accurate  inter- 
pretation of  a  general  rule.  If  we  could  be  content 
to  think  of  Logic  as  merely  a  group  of  rough  maxims 
about  reasoning,  analogous  to  the  maxims  of  conduct 
to  be  found  in  a  copybook,  then  no  douiit  we  might 
learn  the  abstract  definitions  by  heart,  and  so  have 
done  with  them.  A  phrase  like  *'  Evil  communica- 
tions corrupt  good  mannei*s  "  carries  a  rough  meaning 
even  though  we  do  not  inquire  very  precisely  what 
communications  have  a  false  appeannu-o  of  evil.  But 
a  logician,  if  he  cares  about  his  business,  cannot  re- 
main so  easily  content  with  vague  generalisations. 
He  feels  l)ound  to  take  more  trouble  with  the 
doctrines  of  his  special  science.  He  cannot  pretend 
that  there  is  any  reason  for  the  existence  of  Logic,  as 
contrasted  with  mere  common  sense,  if  its  own  rules 
are  left  to  be  interpreted  in  haphazard  fashion  :  in- 
deed the  technicalities  also  would  then  become 
unnecessary,  for  there  is  evidently  no  particular 
merit  in  using  a  pompous  tenn  to  express  merely 
the  same  vague  idea  that  the  man  in  the  street 
expresses  in  simpler  language.  Only  a  sort  of  fair- 
weather  Logic  can  be  made  of  such  materials, — a 
Logic  which  is  applicable  where  no  doubt  or  differ- 
ence of  opinion  has  arisen,  but  which  breaks  down 
exactly  at  the  point  where  the  demand  for  careful 
method  begins.  That  is  why  the  logician  eventually 
gets  drawn  into  the  problems  of  accurate  interpreta- 
tion of  general  rules  in  special  cases ;  is  it  not  better 


CH.I,§8  AIM  AND  METHOD  OF  LOGICAL  STUDY  47 

that  he  should  do  this  willingly  and  with  open  eyes, 
rather  than  be  led  into  the  difficulties  by  accident 
and  then  flounder  into  worse  confusion  in  the  effort 
to  ignore  them?'  Real  difficulties  will  not  allow 
themselves  to  be  concealed  for  ever,  and  especially 
not  in  the  name  of  science. 


§  8.— Definition  and  Translation 

This  view  of  the  way  in  which  technicalities 
should  be  studied  may  be  more  easily  kept  in  mind 
by  means  of  the  distinction  noticed  al)ove  between 
the  two  main  kinds  of  '  definition,' — that  which  gives 
a  general  account  of  the  meaning  of  a  word  and  that 
which  gives  an  account  of  it  with  reference  to  some 
particular  assertion  in  which  it  occurs.  And  for  the 
purpose  of  keeping  this  distinction  clear  the  student 
will  often  find  it  useful  to  call  the  former  kind  of 
definitions  trail  slat  ions,  so  as  to  emphasise  the  fact 
of  their  liability  to   fail  in  removing   a   particular 

'  A  favourite  way  of  seeking  to  rule  these  inquiries  out  of  court  is 
throuf,'h  the  attemi)t  to  regard  Logic  as  having  no  special  interest  in  the  dis- 
tinction hetwecn  good  and  bad  reasoning,  and  so  to  get  rid  of  the  practical 
&s\iect  of  the  science  altogether.  But  some  of  the  writers  who  incline  to 
reconmiend  this  attitude  do  not  restrict  themselves  to  it  in  their  own  works, 
and  the  better  their  work  is  the  less  can  they  do  so.  Even  if  the  central 
problem  were  sUtcd  as  the  study  of  the  nature  of  reasoning,  still  that  would 
involve  a  study  of  the  difference  between  more  and  less  rational  reasoning  as 
its  foundation.  Similarly,  a  study  of  "the  relations  of  propositions  to  'one 
another"  must  base  itself  on  discrimination  of  the  true  relations  from  the 
merely  apjurent.  The  recommendation  to  avoid  all  connection  with  jiractice 
seems  to  be  made  i>artly  in  order  to  guard  beginners  against  a  possible  dis- 
apjKjintment,  and  j>artly  through  some  fear  of  the  science  becoming  degraded. 
Hut  the  word  practical  need  not  always  be  taken  in  its  most  uncompliment- 
ary sense,  and  when  it  is  not  so  taken  the  dislike  of  practical  considerations 
becomes  an  excuse  for  indolent  abstractness  of  theory.  A  system  of 
Logic  wholly  unrelated  to  actual  difficulties  of  reasoning  might  escape  the 
charge  of  being  practical,  but  if  it  were  called  theoretical  it  would  degrade 
that  word  also.  Besides,  there  is  no  doubt  that  Logic,  like  all  other 
sciences,  has  always  been  very  closely  bound  up  with  the  needs  of  practice, 
if  not  entirely  called  into  existence  by  them.  A  Logic  which  quite  con- 
sistently avoided  attempts  to  discriminate  between  good  and  bad  reasonings 
would  be  unlike  any  that  has  yet  been  written. 


48 


USE  OF  WORDS  IN  REASONING        part  i 


r 


L 


difficulty  of  application.  A  general  definition,  just 
because  it  is  general,  must  inevitably  leave  some 
particular  difficulties  untouched.  A  general  definition 
suffers,  like  all  other  general  assertions,  from  the 
defect  of  abstractness. 

The  name  '  translation  '  seems  appropriate  for  the 
following  reasons.  If  we  consider  the  various  ways 
in  which  the  meaning  of  any  word  can  be  verbally 
explained,  three  main  types  stand  out  with  some 
clearness.  At  the  lower  end  of  the  scale,  where 
explanation  is  at  its  vaguest,  there  is  the  kind  of 
statement  that  a  dictionary  gives, — the  translation 
of  a  word  into  more  familiar  language,  as  when 
'  ambiguity  '  is  explained  as  *  double  meaning  '  ;  or 
even  a  mere  hint  of  what  is  intended,  as  when 
'ammonite'  is  explained  as  'a  kind  of  fossil  shell.' 
At  the  other  end  of  the  scale,  w  here  explanation  is 
most  precise  and  definite,  there  is  the  process  of 
discussion  by  which  a  special  difficulty  of  application 
(an  '  ambiguity  '  ^  )  is  dealt  with  after  it  has  arisen. 
And  between  the  two  extreme  types  come  the  better 
kind  of  generally -useful  definitions,  which  have  evi- 
dently something  in  common  with  both  ends  of  the 
scale.  In  face  of  a  particular  difficulty  of  application 
which  they  foresee  and  remove,  they  make  good  their 
claim  to  be  called  definitions ;  in  face  of  a  particular 
difficulty  which  they  do  not  foresee  and  remove,  they 
become,  for  the  time,  analogous  to  translations.  For 
then  they  do  no  more  than  alter  the  verbal  form  of 
the  question  which  states  the  difficulty,  and  so  may 
be  said  to  translate  the  word  rather  than  to  define  it. 
They  give  an  answer  which,  while  pretending  to  be 


*  Tlie  reasons  for  this  accouut  of  the  nature  of  ambiguity  are  given  cliiefly 
in  §§  43-48. 


cu  I,  §  8  AIM  AND  METHOD  OF  LOGICAL  STUDY  49 

relevant,  only  raises  the  old  difficulty  under  another 
name.  If,  for  instance,  you  want  the  word  'luxury' 
4lefined  in  order  to  apply  in  some  doubtful  case  the 
rule  that  luxury  is  to  be  avoided,  it  is  no  use  to  be 
told  that  luxuries  are  the  opposite  of  necessaries. 
That  answer  leaves  your  difficulty  exactly  where  it 
was,  though  it  gives  you  another  verbal  expression  as 
equivalent  to  '  luxury ' ;  and  perhaps  you  knew  as 
much  before.  We  noticed  the  same  thing,  at  p.  30, 
in  the  case  of  the  words  abstract  and  concrete. 

The  turning-point  of  the  distinction  here  intended, 
then,  is  that  a  translation  is  not  wanted  except  when 
the  word  to  be  translated  is  unfamiliar,  while  a 
definition  is  not  w^anted  except  when  the  rough 
meaning  of  the  w^ord  is  already  known, — and  only 
then  if  an  actual  difficulty  is  felt  in  applyino-  the 
word  correctly  in  a  given  case  or  cases.  The  desire 
for  a  translation  is  the  desire  for  a  provisional 
explanation  to  enable  a  start  to  be  made  in  raisino- 
further  inquiries  ;  the  desire  for  a  definition  is  itself 
the  raising  of  the  further  inquiries  which  are  only 
possiI)le  when  a  translation  is  already  possessed. 
Having  thus  drawn  the  distinction  we  may  use  the 
word  '  translation '  rather  than  '  definition  '  either 
when  we  have  to  complain  that  a  given  attempt  to 
define  a  word  does  not  meet  a  particular  difficulty 
vdiich  is  raised,  or  again  when  we  are  stating  a 
definition  which  does  not  claim  to  be  more  than 
generally  useful,  or  useful  for  the  purpose  of  convey- 
ing a  rough  notion  of  the  meaning  to  a  person  to 
whom  the  word,  or  some  technical  usage  of  it,  is 
unfamiliar.  For  the  beginner,  to  whom  the  techni- 
calities of  a  science  are  as  strange  as  words  in  a 
foreign  language,  it  is  often  necessary  to  give  the 


50  USE  OF  WORDS  IX  llEASONISG        parti 

merely  general  detiuitions  first,  and  as  long  as  he  is 
sufficiently  warned  against  supposing  them  to  be 
more  than  roughly  applicable  no  harm  is  likely  to  be 
done. 

§  9._Can  a  Prooressivk  Logic  be  Taught? 

Our  conception  of  the  general  aim  and  method  of 
logical    study    may    now    be  briefly  summarised    as 
follows.      The  one  purpose  of  Logic,  whether  it  be 
called  a  practical  or  a  theoretical  purpose,  is  to  obtain 
insight  into   the  ditt'erence  between    good    and   bad 
reasoning  ;  l)ut  since  this  is  necessarily  a  gradual  and 
progressive  achievement,  and  since  it  is  not  possible 
to  fix  the  date  at  which  we  first  begin  to  obtain  such 
insight,  the  actual  work  of  the  student  of  Logic,  at 
any  stage  of  his  progress,  consists  in  improving  his 
existing  views  little  l)y  little,  rather  than  in  making 
a  sudden   leap'   from  ignorance  to  knowledge,   still 
less  in  learning  '  truths'  which,  if  interpreted  in  the 
only  sense  in  which  they  can  seriously  claim  to  be 
true,    either   answer   no   question    or    else   beg   the 
questions  they  are  supposed  to  answer.     And  since 
such  improvements  involve  changes  in  the  conception 
and  expression  of  doctrines,  questions  as  to  the  precise 
meaning  of  the  technical  terms  which  are  used   to 
express    them     must    constantly   arise,  —  questions 
analogous  to  that  about  the  quasi-explosive  bullets, 
or  to  the  question  whether  a  bicycle  is  or  is  not  a 

1  No  doubt  the  same  appliej?,  strictly  sjieaking,  to  progress  in  any  dei)art- 
ment  of  natural  science.  But  in  many  sciences  the  step  from  popular  to 
scientific  knowledge  is  much  more  abrupt  than  in  Logic,  since  reasoning  is 
a  more  universal  practice  than  reasoning  about  a  particular  group  of  lacts 
such  as  those  considered  {e.q.)  in  Botany  or  Chemistry.  One  may  con- 
tentedly disclaim  all  knowledge  of  a  limited  special  branch  of  inquiry,  but 
we  cannot  so  contentedly  disclaim  all  knowledge  of  that  which  underlies 
every  science  e«iually— the  distinction  between  good  and  bad  reasoning. 
Inevitably  we  all  know  something  about  it. 


CH.  I,  Ji  9  AIM  AND  METHOD  OF  LOGICAL  STUDY  51 

*  carriage '  within  the  meaning  of  the  Act.  It 
should  never  be  forgotten  that  technical  terms  only 
justify  their  existence  when  they  are  seen  as  instru- 
ments for  expressing  general  rules  with  accuracy. 

Our  reasoned    acceptance  of  these  views  will  of 
course  depend  a  good  deal  upon  the  fuller  meaning  we 
give  them, — upon  the  details  and  corollaries  they  are 
meant  to  include.     And  a  first  corollary  from  them  is 
that  Logic  must  always  be  to  some  extent  at  war 
with  its  own  earlier  stages.     The  logician,  in  so  far  as 
he  attempts  to  be  scientific,   is    constantly   findino- 
previous  or  existing  doctrines  a  little  too  slack  and 
easy,    his   special  business  being   to   guard    against 
cheapness  of  logical  doctrine,    against   attempts   to 
hide  real  difficulties  under  vague  language,  against 
any  delusive  simplification   of     the    work  that   has 
to  be  done.     We  shall  find  it  instructive,  therefore,  in 
discussing  any  particular  logical  doctrine,   to  make 
this  element  in  it  the  centre  of  interest.     And  though 
there  is  room  for  endless  subtlety  in  doing  so,  there 
is  also  at  present  an  obvious  need  for  some  elementary 
criticism.     When  the  grosser  defects  of  our  traditional 
Logic  have  Ijecome  more  widely  recognised  than  is 
now   the   case,    then    the    same     method    will     no 
doubt  be  used  with  beneficial  eff*ect  against  our  own 
results. 

This  consideration — that  the  improvement  of  Loo-ic 
is  an  everlasting  process  and  may  be  made  as  gradual 
as  we  please — allow^s  us  to  hope  that  the  general  view 
here  taken  is  not,  after  all,  incapable  of  adaptation  to 
the  wants  of  the  beginner.  The  difficulty  of  doing  it 
I  should  be  the  first  to  admit,  but  we  need  not  assume 
it  to  be  a  hopeless  undertaking.  In  some  respects 
indeed    our  method  will  be   found   easier  than  the 


i 


J 


52 


USE  OF  WOIWS  IN  REASONING        part  i 


traditional  one,  at  least  by  readers  of  an  inquiring 
turn  of  mind.  Such  readers  always  find  a  great  deal 
of  self-contradiction  and  needless  perplexity  in  the 
traditional  system,  faults  which  may  be  traced  to  a 
few  avoidable  sources.^  Again,  the  inquiring  mind 
is  inclined  to  l)e  suspicious  in  the  presence  of 
technicalities  for  which  no  use  is  apparent,  and  the 
traditional  Logic  is  grievously  overburdened  with 
these ;  it  has  retained  accretions  of  them,  through 
centuries  of  changing  philosophy  and  growing  science, 
without  much  attempt  to  discriminate  between  the 
dead  and  the  living  notions  which  they  imply.  As 
an  exercise  for  the  memory^  they  may  be  useful,  l)ut 
to  those  who  want  to  get  forward  in  knowledge  of 
Logic  many  of  them  are  now  no  mure  than  obstacles 
and  sources  of  error.  Our  method  leaves  these  dead 
and  useless  technicalities  aside  without  the  least 
compunction.  The  simplest  rule  is  that  no  techni- 
cality shall  be  considered  worth  discussing  unless  it 
supplies  an  already  felt  need  in  expressing  a  doctrine, 
and  further,  that  no  doctrine  shall  be  put  forward  for 
acceptance  without  at  the  same  time  attempting  to 
show  its  purpose  and  application, — especially  to  show 
the  plausible  errors  which  it  counteracts. 

The  apparent  defect  of  a  system  of  growing 
truth,  from  the  teacher's  point  of  view,  is  its  lack 
of  rigidity,  of  curtness,  and  of  confident  certainty. 
Teachers  are  fond  of  reminding  us  that  the  l)eginner, 
even  when  he  is  really  seeking  for  knowledge  and 
not   merely  submitting   to   be  crammed,  wants  his 


*  For  a  fjeneral  summary  of  these,  see  chap.  xii. 

2  Of  course  many  of  them  have  also  a  historical  interest,  but  that  aspect 
of  them  is  naturally  never  shown  to  the  beginner.  Indeed,  to  do  so  would 
be  not  only  to  unsettle  his  faith  in  tlieir  present  im}>ortance,  but  to  introduce 
him  to  greater  diliiculties  than  any  here  proj^sed. 


I 


cir.  I,  i^  9  AIM  AND  METHOD  OF  LOGICAL  STUDY  53 

knowledge  in  a  downright  form ;  not  vague  hints  of 
an  elusive  truth  which  is  never  quite  satisfactory, 
but  plain  statements  which  he  can  trust  and  remember 
and  apply.  So  he  does,  no  doubt ;  but  that  hardly 
seems  to  be  an  argument  for  giving  him  statements 
the  plainness  of  which  is  perplexity  disguised  and 
the  matter  of  which  is  either  false  or  wholly  absent. 
There  is  another  way  of  giving  him  what  he  legiti- 
mately wants.  If  we  at  first  restrict  him  to  negative 
doctrines — i.e,  to  those  which  point  out  that  such 
and  such  accepted  views  are  in  need  of  certain 
corrections— we  can  get  plenty  of  them  which  are 
capable  of  fairly  plain  statement  and  simple  applica- 
tion with  the  licst  results.  Since  the  beirinner's 
mind  is  not  a  blank  sheet  of  paper  in  regard  to 
logical  knowledge,  but  a  storehouse  of  vague  and 
erroneous  generalisations,  the  process  of  learning 
Logic  is  for  him  in  the  first  place  a  process  of  un- 
learning things  he  has  taken  for  true. 

The  first  two  parts  of  this  book  will  therefore 
contain  an  examination  of  various  common-sense  and 
traditional  views  about  the  use  of  words  in  assertion 
and  reasoning,  and  wdll  make  an  attempt  to  show  the 
more  important  errors  in  them,  to  notice  the  point  at 
which  each  of  them  breaks  down  and  becomes  mis- 
leading. In  this  way  the  student  will  not  only  have 
something  to  take  hold  of  at  once,  but  will  also  find 
that  the  attempt  to  rectify  his  views  on  these  subjects 
may  later  lead  him  just  as  far  as  he  chooses  to  go 
into  the  depths  of  philosophy.  There  is  no  pressing 
need  to  go  to  the  end  ;  in  fact  no  one  has  ever  done 
so,  and  yet  mankind  thrives  and  progresses  in  know- 
ledge. But  at  every  step  of  the  way  something  is 
gained.     For  the  harm  of  *'  a  little  know^ledge  "  does 


54 


USE  OF  WORDS  IN  REASONING        part  i 


not  consist  in  its  being  little  but  in  its  being  taken 
for  more  than  it  is  worth.  On  our  plan  this  clanger 
is  specially  fought  against  from  the  beginning. 
There  is  here  no  attempt  to  put  into  the  hands  of 
inexperienced  young  people  a  perfect  system  by 
which  they  can  test  all  the  arguments  they  meet 
with  and  see  at  once  which  are  sound  and  which 
fallacious ;  the  only  attempt  worth  making  is  that 
of  directing  and  helping  forward  the  natural  process 
of  gradually  gaining  insight  into  this  difficult  dis- 
tinction. The  student  may  be  safely  warned  from 
the  first  that  Logic  is  not  a  subject  to  be  learnt  and 
done  with,  Ijut  a  life-long  study  as  endless  as  any 
other  branch  of  science.  He  may  safely  be  warned 
from  the  first  that  there  is  no  such  tiling;  as  *  lofjical 
proof  in  the  sense  of  finally  conclusive  proof,  or  as 
sharply  contrasted  with  inferior  kinds  ;  but  that  in 
all  reasoning  about  matters  of  fact  the  most  we  can 
do  is  to  guard  against  those  sources  of  error  which 
our  previous  experience — illumined  l)y  our  Logic — 
may  have  brought  to  our  notice.  A  little  knowledge 
of  this  kind  can  hardly  be  called  a  dangerous  thing. 

And  another  somewhat  similar  truth  should  also 
be  of  use  to  the  beginner.  He  must  not  suppose 
that  the  cautious  and  minute  inquiries  of  Logic,  or 
of  science  generally,  are  always  appropriate  w^hen  an 
opinion  has  to  be  formed.  The  chief  occasion  on 
which  they  lose  their  value  is  when  there  is  need  for 
hurry,  or  rather  wherever  time  is  of  more  importance 
than  minute  accuracy.  Since  everyday  life  is  full  of 
such  occasions  it  is  well  to  remember  that  the  study 
of  Logic  is  not  the  only  valuable  mental  training. 
It  cannot,  for  instance,  be  of  much  use  in  warfare  or 
in  business  affairs  generally.     By  keeping  this  warn- 


CH.  I,  §  9  AIM  AND  METHOD  OF  LOGICAL  STUDY  55 

ing  in  view  we  may  avoid  the  special  harm  w^hich 
belongs  to  the  sceptical  hal)it  of  mind, — excessive 
indecision  or  slowness  in  reaching  conclusions.  It  is 
quite  possil}le  to  distinguish  sufficiently  in  practice 
lietween  questions  which  need  a  prompt  answer 
approximately  correct  and  those  in  which  we  may 
be  content  with  a  never-ending  search  for  greater 
accuracy  and  fulness.  We  are  not  always  compelled 
to  hold  a  strong  opinion  prematurely. 

Some  warning  should  also  V)e  given  against  the 
natural  supposition  that  in  studying  Logic  w^e  are 
learning  how  to  conduct  a  controversy.  Indirectly, 
but  only  quite  indirectly,  knowledge  of  Logic  may  be 
useful  for  this  purpose ;  l)ut  the  art  of  disputing  or 
convincing  depends  on  many  other  things  as  well, 
and  (so  far  as  it  can  l)e  studied  at  all)  deserves  a 
separate  treatment,  with  the  purely  logical  element 
in  it  reduced  to  small  dimensions.  This  subject 
receives  some  attention  in  American  colleges,^  but 
has  not  yet,  I  l)elieve,  become  a  Ijranch  of  academic 
instruction  in  England ;  and  obviously  it  has  the 
special  kind  of  difficulty  that  belongs  to  an  art,  so 
far  as  an  art  can  be  contrasted  with  a  science.  Skilful 
oratory,  or  even  effective  argument,  needs  a  richer 
combination  of  qualities  than  is  demanded  for  the 
study  of  the  use  of  words  in  reasoning,  or  indeed  for 
any  philosophical  work.  Such  useful  controversial 
virtues,  for  instance,  as  moderation  and  self-control 
evidently  cannot  be  acquired  by  the  mere  study  of 
Logic,  how^ever  laboured.  They  come  to  us  rather 
by  character,  and  experience,  and  partly  through  a 
sense  of  humour. 

*  Of  books  intended  for  this  purpose  the  only  one  I  happen  to  know  is 
The  Principles  of  Artjimicntfttion  by  Prof.  Baker  of  Harvard. 


56  USE  OF  WORDS  IX  liEASOXIXG        parti 

What  value,  then,  remains  for  Logic,  and  why 
should  any  one  care  to   study  it  ?      That  is  easily 
answered  if  we  admit  that  there  are  any  occasions  on 
which  it  is  worth  while  to  know  more  about  the  differ- 
ence  between  good  and  bad  reasoning  than  our  unaided 
common  sense  can  tell  us ;  for  it  is  exactly  on  these 
occasions,  and  on  no  others,  that  Logic  is  wanted. 
If  there   is   any   one    who    would   deny   that    such 
occasions  ever  occur,  lie  would  also  deny  the  practical 
value   of  Logic.      j\Iost   people,    however,    know  at 
least    that    the   case   does   arise    occasionally,    even 
though    they    fail   to    recognise    its    frequency    and 
importance.      That   recognition    can    only   come    by 
degrees,  but  it  is  certain  to  come  to  those  who  will 
make  any  attempt  to  study  Logic  as  a  progressive 
science,  and  it  is  certain  to  grow  steadily  stronger  the 
further   they   push    the    inquiry.      The   function    of 
Logic  is  to  help  common  sense  in  cases  where  (time 
being  available  for  deliberation)  common  sense  comes 
to  a  difficulty,   a  doubt,  or  a  difference  of  opinion 
which  it  wants  removed;  and  these  cases  are  any- 
thing but  rare.     Indeed  they  are  far  too  common, 
and    the   more   telling    objection    against    accepted 
theories  of    the    difterence  between  good   and    bad 
reasoning  is  not    that  they  are  a  mere  intellectual 
luxury  or  plaything,  or  a  kind  of  knowledge  seldom 
wanted,   but    that  face    to    face  with  the  enormous 
mass  of  difference  of  opinion  which  exists  even  where 
neither    passion    nor    hurry    is  a  disturbing    factor, 
our  best  Logic  is  as  yet  so  limited  in  its  power  of 
dealing    with  it.      On   this    ground    alone    there    is 
always  a  crying  need  for  common  sense  to  improve 
its   logical   views.      And    the   improvement   cannot 
even  be  begun  until  we  admit  their  unfinished,  pro- 


f 


CH.  I,  .^  9  ALU  AND  METHOD  OF  LOGICAL  STUDY  57 

gressive  character.  We  must  recognise  that  at  any 
period  their  defect  is  essentially  that  which  attaches 
to  a  rule  of  thumb,  or  to  any  generalisation  which, 
l)ecause  it  is  only  roughly  true,  is  found  to  be  too 
rigid  for  satisfactory  application  to  the  real  difficulties 
of  reasoniiif;. 


CHAPTER   II 


REASONING   AND    SYLLOGISM 


§  10.— Kkflfxtivk  and  Forward  Reasoning 

*  Reasoning  '  is  a  word  which  scarcely  needs  transla- 
tion, and  wliich  (as  we  shall  have  to  confess  in  chap, 
iv.)  is  extremely  difficult  to  define.  But  we  may 
leave  the  difficulties  of  its  definition  aside  for  the 
present  and  attempt  to  get  a  general  view  of  the 
nature  of  the  process  in  cases  where  no  one  would  be 
likely  to  raise  any  doubts  as  to  their  being  examples 
of  reasoning  rather  than  of  '  instinct/  or  of  '  un- 
reasoned judgment.* 

One  small  difficulty  should  however  be  mentioned, 
since  it  belongs  merely  to  the  translation.  There  are 
in  common  use  two  different  senses  of  the  word, — 
different  and  yet  so  closely  connected  that  confusion 
often  results.  *  Reasoning '  may  mean  arguing  (with 
oneself  or  with  others)  about  the  truth  of  a  given 
assertion,  or  on  the  other  hand  it  may  mean  using 
an  already  accepted  truth  as  a  stepping-stone  to  some 
further  truth  less  obvious.  That  is  to  say,  both  the 
reflective  movement  of  thought  which  seeks  to  dispute 
or  justify  a  conclusion  already  formed,  and  the  for- 
ward movement  of  thought  which  seeks  to  reach  a 
new  conclusion,  are  constantly  included  and  confused 


PT.  I,  CH.  n,  §  10  REASONING  AND  SYLLOGISM         59 

under  the  vague  term  reasoning  or  inference.^     The 
confusion  is  a  natural  one  and  yet  avoidable.     It  is 
partly  due  to  the  fact  that  reflection  enters  so  largely 
into  the  forward  movement  itself.     As  will  be  seen 
in   chap,    iv.,    it  is  far  from  certain   that   there   is 
any  judgment'   from   which    reflection    is    entirely 
absent.     And,  however  this  be  settled,  at  any  rate  re- 
flection obviously  enters  into  a  large  number  of  our 
judgments  in  the  very  process  of  their  formation,— 
namely  into   all  those   where  we  really  care   about 
judging  correctly  and  are  not  compelled  to  judge  in 
too  great  a  hurry.     This  aspect  of  reasoning  has  there- 
fore a  special  interest  for  Logic,  and  in  the  present 
chapter  we  shall  confine  attention  to  it  exclusively ; 
we  shall  here  think  of  reasoning  purely  as  a  reflective 
process,  where  an  assertion  is  on  its  trial  and  reasons 
are  given  for  accepting  or  rejecting  it.    While  forward 
reasoning   starts   from  fiicts  accepted    as    true,  and 
asks  what  unseen  conclusion  they  point  to,  reflective 
reasoning  starts   from  a   questioned   conclusion   and 
examines  its  truth  by  exploring  its  grounds. 

§  11- — How  Conclusions  are  Supported 

What  do  we  all  know  about  this  operation,  without 
the  aid  of  a  technical  Logic  ?  It  is  familiar  to  us 
from  childhood,  and  we  can  scarcely  avoid  some 
knowledge  of  it.  We  know,  for  instance,  that  to 
question  the  truth  of  a  conclusion  is  to  call  for  facts 

»  Through  failing'  to  avoid  this  confusion  we  might  easily  reach  the 
paradox  that  reasoning  involves  two  incompatible  things,— novelty,  and  the 
absence  of  novelty,  in  the  conclusion.  See  an  article  by  Miss  Jones  in  Mind 
for  April  1898. 

«  The   word   'judgment*    may   often    conveniently   be   used    instead   of 

'assertion,'  where  we  want  to  speak  of  the  assertion  as  accepted  by  oneself 

instead  of  as  made  to  an  audience.     On  any  occasion  when  a  difference  is 

recognised   between  a  judgment  and  an   assertion,    the  former  means   'the 

assertion,  expressed  or  not,'  and  the  latter  'the  judgment  expressed.' 


60 


USE  OF  WORDS  IX  REASONING 


PART  I 


on  which  it  may  rest,  and  that  to  support  a  conclu- 
sion is  to  produce  such  facts.     We  know  also  that 
after  the  facts  are  produced  they  may  still  be  open  to 
objection  on  one  of  two  grounds ;  we  may  dispute 
their  truth,  or  we  may  dispute  their  relevance, — their 
sufficiency  (even   if  true)   to   prove   the  conclusion. 
And  whichever  line  of  objection   is  adopted  a  new 
question  is  thereby  raised,  which  takes  precedence  of 
the   question   originally    in   dispute.      Till  this  new 
question  is  answered  the  argument  is  at  a  standstill  ; 
and,  notoriously,  the  end  of  an  argument  may  take  a 
long  time  to  reach,  for  one  question  only  too  often 
leads  to  another.    The  original  question  depends  upon 
a  second  question,  and  that  may  in  turn  depend  on  a 
third,  and  so  on  until  we  either  give  up  the  argument 
in  despair  or  accept  the  new  light  which  our  opponent 
has   been   trying  to  give  us.     Again,   we  all  know 
something  about  what  constitutes  the  relevance  or 
sufficiency  of  an  accepted  fact  to  prove  a  conclusion  ; 
and  something  also  of  what  is  involved  in  the  claim 
that  a  fact  is  *  true.'    ]\Iore  or  less  vaguely  we  know — 
thougli   we  often  cannot  express  the  knowledge  in 
any  satisfactory  general  language — that  to  recognise 
given  facts  as  relevant  to  given  conclusions  is  the 
same   thing   as  to  recognise   principles  and  general 
rules,  especially  rules  about  the  way  things  happen 
in   Nature,  —  rules    of    *  causation '    or    of    *  causal 
sequence,'   as   they  are  sometimes   called.       For  in- 
stance, the  rising  and  falling  barometer  is  taken  to  be 
a  relevant  fact  in  weather  prediction  just  in  so  far  as 
we  believe  in  general  rules  connecting  tliese  variations 
with  particular  kinds  of  weather  ;  if  we  hold  that  the 
rules  are  vague  and  liable  to  exceptions  we  see  at 
once  that  the  use  of  them  in  a  special  case  is  uncer- 


CH.H,.^12     REASONING  AND  SYLLOGISM  61 

tain,  while  if  we  are  contemplating  some  rule  without 
exceptions— like  '  any  two  sides  of  a  triangle  are 
together  greater  than  the  third  side  '—then  no  such 
difficulty  in  its  application  arises.  And  we  constantly 
act  on  the  assumption  that  the  remedy  for  vagueness 
in  our  general  rules  is  to  look  for  the  causation  behind 
them,  as  far  as  we  can,— to  see,  for  instance,  why  i\ie 
falling  barometer  and  the  coming  storm  are  connected 
facts ;  for  that  is  always  a  help  to  us  in  seeing  what 
the  exceptions  to  the  rule  are  likely  to  be.  Thus 
(when  once  the  point  at  issue  is  clear)  argument 
between  two  persons,  or  difference  of  opinion  as  to 
the  soundness  of  a  piece  of  attempted  proof,  is  o-ene- 
rally  found  to  turn  upon  some  difl'erence  of  view  as  to 
the  way  things  happen  in  Nature,  and  the  consequent 
meaning  of  this  or  that  fact,— the  precise  interpreta- 
tion that  ought  to  be  put  upon  it.  The  more  com- 
plete our  general  knowledge  is,  the  more  we  are  able 
to  '  take  facts  for  what  they  are  worth '  and  so  to 
avoid  putting  a  wrong  construction  upon  them. 


§  12. — The  Syllogistic  Framework 

At  least  so  much,  I  think,  is  fairly  well  known  to 
most  people  before  they  begin  the  technical  study  of 
Logic.  And  part  of  the  business  of  Logic  is  to  make 
this  somewhat  vague  knowledge  more  definite  and 
consistent.  Its  earliest  answer  to  the  problem  sur- 
vives almost  unaltered  in  the  traditional  doctrine  of 
the  Syllogism,  which  involves  the  supposition  that 
every  assertion,  regarded  as  disputable,  requires  for  its 
proof  two  others  related  to  it  in  a  particular  manner 
and  accepted  as  true.  These  are  called  respectively 
the  *  major  premiss '  and  the  '  minor  premiss ' ;  the 


1 


62 


USE  OF  WORDS  IS  IIKASOXING         PAiiTi 


assertion  supposed  to  he  proved  l)y  them  is  called  the 
'  couclusioii ' ;  and  the  three  assertions  together  form 
a  *  syllogism.'  The  particular  relation  require«l 
between  the  premisses  and  the  conclusion  may  be 
seen  with  the  help  of  the  old  typical  ^  instance : 
Socrates  is  mortal  (conclusion)  for  he  is  a  man 
(minor  premiss),  and  all  men  are  mortal  (major 
premiss).  Keeping  this  instance  in  view  we  see  that 
reflective  'syllogising'  consists  in  showing  the  con- 
elusion  as  a  particular  case  coming  under  a  geiitral 
rule.  In  the  typical  syllogism  the  statement  of  the 
freneral  rule  is  the  major  premiss,  and  the  function  of 
the  minor  premiss  is  to  connect  the  conclusion  with  it. 
Now  we  may  admit  from  the  first  that  the  simpler 
an  argument  is  the  more  easily  can  this  elementary 
conception  be  applied  to  it.  For  instance,  suppose 
that  in  order  to  prove  that  the  lines  AB  and  AC  are 
equal  you  bring  forward  the  fact  that  they  are  radii 
of  the  same  circle.  Then  it  is  plain  that  the  relevance 
of  this  fact  depends  on  the  assumption  of  the  general 
rule  that  all  radii  of  the  same  circle  are  equal.  Here 
we  have  an  extreme  case  of  simplicity  in  an  argument  ; 
the  fact  brought  forward  is  remarkably  definite,  and 
is  at  once  connected  with  a  familiar  generalisation 
which   exactly   covers    the    assertion    you    wish    to 

I  The  tr!vliti»)nal  Logic,  wliile  recognising  this  form  .is  typical,  intro<luce.s 
a  number  of  verbal  complications  through  identifying  the  sentence  with  the 
assertion  and  so  recognising  ditVerences  which  are  merely  of  form,  an<l  not  of 
meaning.  These  are  irrelevant  to  anything  we  have  here  to  say  about  the 
Syllogism,  and  may  be  entirely  dismissed  from  our  thoughts.  Kven  Formal 
Logic  adniits  that  the  value  uf  the  syllogistic  process  stands  or  falls  by  that 

of  its  typical  form. 

As  noticed  in  last  chapter  (p.  11),  logicians  have  a  convenient  custom 
of  still  further  typifying  (or  generalising)  arguments  by  using  letters  instead 
of  words;  for  insUnce,  the  letters  XYZ  or  the  letters  SMP.  Thus  th- 
typical  syllogism  is  often  written  :  '  S  is  P  ;  for  S  is  M,  and  all  M  are  P.' 
Here  S  and  P  stand  for  Subject  ami  Predicate  of  the  conclusion,  and  M  for 
•  middle  term.'  The  nature  of  the  middle  term  will  appear  as  we  i>roceed. 
For  lirst  mention  of  it,  see  note,  p.  tit). 


CH.ii,§l2     REASONING  AND  SYLLOGISM  63 

prove.  The  result  is  a  plain  straightforward  syllogism, 
of  which  the  fact  produced  is  the  minor  premiss?  and 
the  major  premiss  is  the  rule  which  is  clearly  implied 
in  producing  that  fact  for  the  purpose. 

But  arguments  in  general— and  especially  those 

that  are  less  easily  settled— are  seldom  capable  of 

being  reduced  so  readily  to  the  direct  syllogistic  form, 

except  at  a  risk  of  misrepresentation.     We  need  not 

here  dwell  on  the  notoriously  common  difficulty  of 

settling  precisely  what  the  disputed  conclusion  is,— 

since  that  may  be  regarded  rather  as  a  preliminary 

to  reflective  reasoning  than  as  a  part  of  the  process 

Itself.     We  may  imagine  a  clear  point  at  issue  raised, 

and  consider  what  the  special  difficulty  is  that  has 

still  to  be  surmounted  before  the  argument  as  a  whole 

can  be  viewed  as  a  syllogism. 

A  distinctive  feature  of  the  kind  of  arguments  we 
are  here  speaking  of— the  arguments  which  are  less 
easily  settled— is  that  they  do  not  turn  upon  the 
truth  and  relevance  of  a  single  fact,  but  upon  the 
truth  and  combined  relevance  of  many.  This  is  only 
a  loose  way  of  expressing  the  difference,  since— as  we 

shall  presently  have  opportunities  of  seeing it  is  by 

no  means  an  easy  question  what  facts,  if  any,  are 
really  single  or  simple.  But  the  looseness  of  the  ex- 
pression  does  no  harm  so  long  as  we  take  it  as  mean- 
ing only  that  recognised  complexity  in  the  *fact 
produced'— I.e.  in  the  minor  premiss— is  the  dis- 
tinguishing  feature  of  this  kind  of  argument ;  for  it 
is  evidently  a  verbal  accident  whether  we  speak  of 
such  minor  premiss  as  stating  one  complex  fact  or  a 
number  of  simpler  ones ;  our  choice  of  one  or  the 
other  of  these  two  expressions  being  chiefly  a  question 
of  convenience,  of  using  language  so  as  not  to  strain  it 


64  USE  OF  WOBDS  IN  liEASONING        parti 

pedantically  or  without  sufficient  excuse.  What  is 
meant  is  that  the  truth  of  the  conclusion  in  such 
cases  cannot  be  satisfactorily  made  to  turn  on  some 
one  straightforward  concise  statement  of  fact,  like 
"  they  are  radii  of  the  same  circle,"  or  on  some  one 
easily  performed  experiment  which  gives  a  clear  and 
conclusive  answer ;  l)ut  it  involves  the  separation  of 
a  condensed  and  obscure  statement  into  a  number  of 
details  covered  by  it,  or  a  weighing  of  many  facts 
one  against  another  and  a  somewhat  risky  estimate 

of  the  total  balance. 

We  must  all  admit,  I  think,  that  there  are  argu- 
ments of  this  nature.     In  deep  and  persistently  con- 
troversial subjects  of  discussion  we  are  always  meeting 
with  them.     But  they  are  to  be  found  also,  if  we 
care  to  find  them,  in  more  everyday  questions,— at 
least  where  there  is  a  desire  for  accuracy,  and  time  to 
consider  the  question  fairly.     For  instance,  even  in 
such   a  common   matter  as  weather  prediction  it  is 
evident  that   the   usual  simplicity  of  the  reasoning 
depends  on  our  usual  inditlerence.     When  it  is  only 
a  question  whether  to  take  an  umbrella  or  not,  we 
may  rap  the  barometer  and  follow  its  advice ;  while 
if  we  have  the  safety  of  ships  or  harvests  at  stake  we 
go  to  work  more  carefully,— we  collect  a  large  number 
of  separate  details  and  put  them  together  in  the  form 
of  a  chart  in  the  daily  papers.     And  the  interested 
fisherman  or  farmer  goes  a  step  further  and  observes 
for  himself  a  number  of  details  in  the  appearance  of 
his  local  sky  and  the  sequence  of  its  changes,  the 
direction  and  fluctuation  of  the  wind,  and  in  short 
as  many  other  signs  as  he  believes  in.     The  end  of 
the  process  of  collecting  relevant  details  is  wherever 
we  choose  to  stop. 


CH.  n,  §  12     REASONING  AND  SYLLOGISM 


65 


Now  the  question  is  how  arguments  of  this  kind 
are  to  be  explained  as  cases  of  syllogism.  Imagine 
the  difficulty  of  finding  a  major  premiss  to  fit  such 
a  complicated  *  fact '  as  even  the  present  state  of  the 
local  weather  conditions, — finding  any  one  general 
rule  which  shall  exactly  cover  this  particular  case  in 
all  its  details.  I  do  not  mean  only  the  grammatical 
or  literary  difficulty  of  framing  the  sentence  required 
to  express  it,^  but  the  deeper  difficulty  of  obtaining 
any  more  credence  for  it  than  for  the  conclusion  itself. 
An  appeal  to  a  major  premiss  in  support  of  a  doubtful 
conclusion  assumes,  of  course,  that  the  truth  of  the 
major  premiss  is  easier  to  admit  than  that  of  the 
conclusion ;  the  appeal  is  made  to  our  stored-up 
knowledge,  and  its  eft'ectiveness  for  the  purpose  de- 
pends on  the  ease  with  whicli  we  can  recognise  the 
major  premiss  as  an  already  admitted  truth, — like 
''  all  men  are  mortal,"  or  *'  all  radii  of  the  same  circle 
are  ecjual."  But  this  effect  is  lost  if  the  major  premiss 
comes  at  all  under  suspicion  of  having  been  manu- 
factured on  the  spot  in  order  to  fit  a  special  observed 
conjunction  of  facts.  The  more  complex  or  numerous 
these  are  the  more  unlikely  it  is  that  the  precise 
total  conjunction  has  ever  before  been  met  wnth,  and 
the  more  impossible  it  becomes  therefore  to  view  the 
generalisation  about  it  as  part  of  our  stored-up  know- 
ledge.    The  weather-rules  that  we  do  (with  reserva- 

I  There  are  many  forms  of  argument  whose  apparent  unlikeness  to  syl- 
lo^'isnis  is  due  to  the  difficulty  of  ex})re.ssing  their  major  premisses  in  a  &h&\ye 
which  our  grammatical  sense  of  decency  can  abide.  See,  for  instance,  the 
lirst  five  of  the  tight  tyf^es  noted  by  Mr.  Bradley  in  his  Principles  of  Logic, 
p.  226.  Thus,  however  unbearable  may  be  the  sentence  {ibid.  p.  227),  "A 
iKxiy  is  to  the  right  of  that  which  that  which  it  is  to  the  right  of 'is  to 
the  right  of,"  no  one  who  has  the  patience  to  struggle  with  its  interpreta- 
tion would  dispute  its  truth.  Such  principles  are  habitually  used  without 
attempting  to  shock  the  grammarian  by  expressing  them  in  '  logical  form '  ; 
their  truth  is  too  obvious  to  make  the  literary  problem  of  expressing  them 
worth  the  trouble  of  solving. 


66 


USE  OF  WORDS  IN  REASONING        part  i 


tions)  believe  in  are  all  of  a  vaguer,  broader,  simpler 
kind.  Parts  of  the  total  fact  may  fit  into  some  of 
them,  but  the  fact  as  a  whole  cannot  be  seen  as  a 
particular  case  of  any  single  general  rule. 

This  analysis  of  an  argument  into  its  component 
parts — this  l)reaking  up  of  a  syllogism  into  syllogistic 
fragments — is  the  only  known  method  of  examining 
the  truth  of  a  conclusion  which  professes  to  rest  upon 
stated  reasons.  Both  carelessness  and  t^enius  mav 
dispense  with  it,  and  so  jump  to  conclusions,  but  if 
we  wish  to  know  in  the  case  of  a  given  conclusion 
what  part  has  l)een  played  in  it  by  carelessness  and 
genius  respectively,  we  must  pull  the  reasoning  to 
pieces  and  look  at  its  separate  threads ;  and  this  is 
not  always  an  easy  operation.  In  the  example  just 
referred  to  the  complexity  is  of  a  kind  that  stares  us 
in  the  face,  but  that  it  cannot  always  be  so  plainly 
seen  is  proved  by  the  fact  that  in  the  course  of  such 
analysis  we  often  discover  the  need  for  carrying  it 
further  than  we  at  first  expected ;  the  limits  we  set 
to  the  analysis  are  dependent  on  the  state  of  our 
existing  knowledge,  w^hich  is  capable  of  growth  ;  and 
wherever  we  set  the  limit  we  claim  to  have  got  down 
to  facts  which  may  safely  be  taken  for  simple.  It  is 
precisely  in  this  claim  that  the  chief  danger  of  faulty 
reasoning  resides.  A  concealed  complexity  in  the 
fact  appealed  to  as  evidence  is  the  root  of  the  defect 
technically  called  '  ambiguity  of  the  middle  term,'  ^ — 
that  last  infirmity  to  which  even  the  most  apparently 

*  The  analysis  of  propositions  into  terms  is  a  nmtter  which  need  not  h<'re 
be  considered,  thongli  something  is  said  about  it  in  §§  .JO,  57,  and  60. 
Meanwhile  it  is  enough  to  know  that  the  'middle  term'  of  a  syllogism  is  that 
{>art  of  the  two  premisses  which  connects  them  with  each  other.  And  since 
the  relation  between  the  two  premisses  is  always  that  of  rule  and  application 
(see  also  note,  p.  72)  it  follows  that  the  account  given  of  the  fact  relied  upon 
as  evidence  is  always  the  middle  term  wherever  the  process  can  be  regarded 
as  a  syllogism  at  all. 


CH.  n,  i^  13     REASONING  AND  SYLLOGISM  67 

faultless  syllogisms  are  liable.  In  an  argument  where 
the  complexity  of  the  minor  premiss  is  so  easily  seen 
that  neither  party  attempts  to  view  the  process  as  a 
single  syllogism  this  chief  danger  of  faulty  reasoning 
does  not  arise,  for  everyone  then  knows  that  much 
remains  to  be  done  before  proof  or  disproof  is  reached. 
To  admit  that  you  have  only  partly  solved  a  complex 
(juestion  is  to  reserve  judgment,  to  recognise  that 
your  conclusion— if  you  incline  to  one  at  all— is 
tentative  and  open  to  revision.  Far  otherwise  is 
it  however  with  the  separate  parts  into  which  you 
have  resolved  the  total  question  ;  for  there  you  have 
got  pieces  .of  argument  resting  on  facts  which,  from 
the  nature  of  the  case,  you  regard  as  simple,— simple 
enough,  at  least,  to  be  taken  as  wholes  without 
discoverable  risk  of  error. 


S  13.— Verbal  Simplicity  of  the  Middle  Term 

It  is  in  our  habit  of  viewing  facts   which  admit 
of  being  concisely  described,    as   simple  facts,   that 
the  danger  chiefly   resides;    and  the  convenience- 
amounting  in  some  cases  to  little  short  of  necessity 
—  which    justifies   this    habit   merely   increases    its 
effective  misleading  power.     No  one,  perhaps,  would 
go  so  far  as  to  say  that  every  fact  describable  by  a 
single  name  is  a  single  fact  rather  than  a  group  of 
facts,  but  our  inclination   to  make  this  assumption 
tacitly  is  at  least  strong  enough  to  cause  considerable 
error.      Our  natural  tendency,   when  our  reflective 
power  is  weak  or  inexperienced,  is  to  fall  under  the 
<lomination  of  words, — a   tendency  which   may   be 
observed  both  in  the  individual  and  in  the  human 
race.      This  superstitious  attitude  towards  language 


68 


USE  OF  WORDS  IN  REASONING        part  i 


shows  itself  in  many  forms,  but  the  one  we  are  here 
concerned  with  is  the  inclination  not  to  suspect  a 
middle  term  of  ambiguity.  The  particular  case  S  is 
seen  as  M,  and  if  we  accept  as  true  the  statement 
that  all  M  are  P,  we  consider  it  proved  that  S  is  P. 
If  we  can  connect  two  premisses  by  a  middle  term 
which,  being  a  single  word  or  a  concise  expression, 
looks  simple,  our  easy-going  childish  or  mediaeval 
Logic  is  satisfied.  We  do  not,  at  first,  look  behind 
words  to  the  precise  details  they  are  meant  to  cover, 
and  so  we  tend  to  overlook  differences  in  meaning 
between  the  middle  term  as  used  in  the  two  premisses 
respectively.  And  thus  one  of  the  chief  sources  of 
false  ideas  about  the  Syllogism  is  the  supposition 
that  *  logi(uil  proof  (or  syllogistic  demonstration) 
gives  certainty, — in  the  sense  that  by  finding  a  pair 
of  accepted  premisses  from  which  your  conclusion  is 
logically  deducible  you  can  force  an  opponent  to 
admit  it,  under  pain  of  becoming  a  sort  of  logical 
outcast.  Logical  outcasts  there  may  indeed  be,  but 
your  opponent  does  not  become  one  by  merely 
admitting  a  pair  of  sentences  while  refusing  to 
admit  a  conclusion  that  *  lo<^ically  follows  *  from 
them ;  what  would  make  him  an  outcast  would  be 
his  shirking  the  question  what  the  ambiguity  is  that 
stands  in  his  way.  His  legitimate  position  is,  *'  I 
admit  that  in  a  sense  M  is  P,  and  S  is  M ;  but  not 
in  the  sense  in  which  they  support  your  conclusion  "  ; 
and  it  is  only  if  he  wishes  to  run  away  after  saying 
this  that  he  can  properly  be  accused  of  shufHing. 
If  he  believes  his  objection  justified  he  will  naturally 
stay  and  explain  it. 

The  concealment  of  real  complexity  under  verbal 
simplicity  is  one  of  the  most  ubiquitous  and  familiar 


<H.  II,  .^  13     REAS(fXIXG  AND  SYLLOGISM 


69 


facts  of  language.  Language  is  full  of  comprehensive 
words  and  phrases  intended  to  mask  and  obliterate 
unimportant  details  and  refer  to  an  underlying 
unity ;  and  such  words  may  perform  their  function 
of  hiding  details  just  as  completely  when  the  details 
are  important  as  when  they  are  not  so.  Take  a 
word  like  man,  or  a  phrase  like  radius  of  a  circle. 
Socrates  is  not  *  man '  in  the  abstract,  but  a  concrete 
individual ;  only  it  happens  that  none  of  his  in- 
dividual peculiarities  are  of  the  smallest  account  as 
against  the  rule  that  man  is  mortal.  And  radii  of 
a  circle  differ  infinitely  in  direction,  but  since  it  is 
clear  that  their  direction  does  not  affect  their  length 
we  proceed  w^ith  confidence  to  recognise  the  equality  of 
any  two  of  them.  On  the  other  hand  let  us  imagine 
the  details  of  the  present  weather  conditions  summed 
up  in  tlie  phrase  that  the  sky  *  looks  threatening,'  and 
we  find  at  once  a  suspicious  kind  of  vagueness  in  the 
description.  By  using  a  comprehensive  phrase  we 
have  simplified  our  major  premiss,  but  in  this 
instance  every  one  can  see  that  it  is  a  purely  artificial 
simplification  and  possibly  delusive.  Evidently  there 
may  be  different  conceptions  of  a  *  threatening ' 
sky,  and  your  conception  of  it  may  not  be  exactly  the 
one  that  the  major  premiss  requires.  The  question 
whether  it  is  so  resolves  itself  inevitably  into  a 
search  among  the  details,  and  then  the  apparent 
simplicity  stands  revealed  as  real  complication. 

Everywhere  in  estimating  the  importance  or  mean- 
ing of  a  fact — that  is  to  say,  its  relevance  to  a  given 
conclusion — the  question  confronts  us  whether  such 
fact  has  been  far  enough  analysed  into  its  details; 
for  of  course  the  weight  of  the  whole  fact  is  only 
another  name  for  the  combined  weight  of  the  details, 


-'■'W 


70 


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CH.  II,  g  14     REASONING  AND  SYLLOGISM 


71 


pro  and  con  ;  and  so  far  as  any  of  these  are  left  out  of 
sight,  risk  of  error  enters  into  our  judgment.  In  the 
examples  just  referred  to,  the  trouble  would  prob- 
ably not  arise;  they  were  chosen  as  well-marked 
instances,  first  of  legitimate  and  secondly  of  question- 
able obliteration  of  details  by  means  of  a  middle 
term ;  in  the  former  kind  there  is  no  risk  to  speak 
of,  and  in  the  latter  the  risk  is  too  obvious  to  be 
effective.  But  evidently  between  the  two  extremes 
there  must  be  a  region  of  cases  less  easily  classed  as 
safe  or  unsafe.  And  these  are  the  cases  that  have 
special  interest  for  scientific  Logic,  since  the  error  in 
them,  if  error  there  be,  is  well  concealed. 

The  importance  of  these  cases  may  be  conceded,  but 
what  about  their  extent,  their  frequency  of  occurrence  ( 
That  is  a  difficult  question  to  answer  shortly,  but  1 
hope  that  in  the  following  chapters  we  shall  find  some 
truths  that  l)ear  upon  it.  The  difficulty  is  to  see  any 
reason,  other  than  merely  accidental, — such  as  the  wish 
to  save  time  or  trouble, — for  putting  a  limit  to  the 
process  of  looking  behind  words  to  the  details  they 
obscure  and  obliterate.  Even  without  attempting  to 
push  the  inquiry  far,  a  little  reflection  shows  at  least 
that  this  misleading  power  of  words  has  a  much  wider 
range  of  action  than  common  sense  is  at  first  inclined 
to  expect.  What  is  a  *  single  '  fact,  when  we  come  to 
consider  the  question  ?  A  fact  with  a  single  name, — 
a  fact  expressible  in  a  short  sentence  ?  That  super- 
stition we  have  just  seen  cannot  seriously  be  defended. 
We  may  rather  ask  whether  any  fact  has  any  other 
singleness  than  this  nominal  or  artificial  kind.  Possibly 
we  shall  find  reasons  for  holding  that  every  *  sinnrle ' 
fiict  is  single  only  so  long  as  we  choose  to  consider  it 
so ;  that  in  all  conception  of  concrete  facts  there  are 


more  and  less  deniable  portions ;  and  that  the  essence 
of  scientific  proof  consists  in  making  the  best  approach 
to  a  clear  separation  of  the  true  and  the  doubtful 
portions  in  any  fact  conceived  as  supporting  a  con- 
clusion. 

For  the  moment,  let  us  anticipate  this  inquiry,  and 
see  what  follows  from  such  a  view  of  the  naturie  of 
facts  in  general.  One  evident  consequence  is  that  the 
correct  reduction  of  arguments  to  the  syllogistic  form 
must  be  difficult  not  only  where  the  plurality  of  the 
facts  is  easily  visible,  but  exactly  as  difficult  in  other 
cases,  and  for  the  same  reason.  In  all  cases,  without 
exception,  the  same  difficulty  in  fitting  the  major 
premiss  to  the  minor  must  be  liable  to  arise, — the 
difficulty  which  we  noticed  in  the  case  of  the  weather- 
signs.  Of  course  there  are  unnumbered  cases  where 
(rightly  or  wrongly)  it  does  not  actually  arise ;  and  if 
we  keep  in  view  only  the  reasonings  of  Euclid,  or 
arguments  aljout  Socrates  and  his  mortality,  we  may 
never  discover  the  need  for  raising  it.  It  is  not  in  easily 
settled  arguments  that  ambiguity  of  the  middle  term 
becomes  a  practical  danger,  nor  in  arguments  that  are 
evidently  vague.  But  if  facts  are  never  single  except 
in  name,  then  there  is  no  descriptive  word  which  is 
perfectly  safe  against  this  kind  of  confusion,  and  those 
that  seem  safest  may  l)e  on  that  very  account  the  most 
effectually  deceitful. 


§  14. — Uses  of  the  Syllogism 

Is  the  Syllogism,  then,  a  wholly  useless  piece  of 
logical  lumber,  like  so  many  other  of  the  old  techni- 
calities? Not  altogether.  The  elaborate  syllogistic 
apparatus  provided  by  the  traditional   Logic  is    no 


i 


72 


USE  OF  WORDS  IN  REASONING        part  i 


CH.  II,  §  U     REASONING  AND  SYLLOGISM 


73 


doubt,  wordy  and  trivial  to  the  last  degree  ;  and  even 
if  we  discard  this  and  keep  only  the  framework  and 
the  leading  idea,  it  is  a  conception  which  cannot  be 
safely  applied  to  actual  arguments  except  by  the  help 
of  experience  and  discretion.  Nevertheless  the  truth 
that  is  in  it  deserves  to  be  recognised,  and,  when  the 
proper  precautions  are  taken,  may  perhaps  be  found 
not  entirely  useless. 

The  leading  idea  of  the  Syllogism,  as  we  noticed  at 
p.  62  above,  is  the  recognition  that  where  any  fact  is 
produced  as  sufficient  to  prove  a  conclusion,  the 
sufficiency  of  such  fact  for  such  purpose  depends  on 
the  acceptance  of  a  generalisation  which  covers  it  and 
connects  it  with  the  conclusion.'     No  doubt  this  is  an 

'  It  should  be  noted  that  there  are  some  arguments  in  Fig.  .*J  which  do 
not  come  at  all  naturally  under  this  conception,  though  they  can  he  forced 
under  it  by  'reduction.*  (Set;  for  instance  Mr.  Bradley's  example  vii.  in 
Primriplcs  of  Lo^fir,  p.  226.  The  function  of  Fig.  :{  is  to  i)rove  '  particular 
propositions,' — which  (see  «?  58  below)  arc  sentence-forms  comnioidy  used  to 
express  the  denial  of  a  (jeneralUation,  rather  than  a  predication  about  a 
Subject.  Thus  'Some  S  are  not  P'  is  more  commonly  intended  as  a  bare 
denial  of  'AH  S  are  P*  than  as  a  predication  about  'Some  8.'  For  vague 
and  negative  conclusions  of  this  kind  the  essential  re«juisite  is  the  production 
of  at  least  one  instance  which  contradicts  the  generalisation  {e.g.  *  M  is  not 
P,  and  M  is  S  ').  Of  course  the  whole  of  M  must  be  outside  P  in  onler  to  get 
the  recjuired  connection  through  the  middle  term  ;  but  since  it  niakes  no 
difference  whether  M  is  a  class  or  an  individual  case,  it  seems  a  straining  of 
language  to  regard  the  major  premiss  in  these  cases  as  necessarily  a  statement 
of  general  rule. 

And  the  so-called  e([uational  syllogisms  are  another  kind  that  do  not 
come  easily  under  the  conception  of  rule  and  application  ;  the  reason  Ijeing 
that  the  sign  =  is  expressly  intended  to  mean  something  different  from  the 
ordinary  copula.  No  doubt  '  A  =  B  '  might  conceivably  mean  '  A  is  so  far 
like  the  recognised  members  of  the  class  B  that  it  may  be  reckoned  among 
them  '  ;  but  as  a  matter  of  fact  Jevons  and  others  have  always  professed  to 
mean  by  it  either  'The  same  identical  thing  (or  class)  may  be  called 
indifferently  either  A  or  B,'  or  else  '  The  two  things  A  and  B  are  identical 
in  some  particular  respect '—^.gr.  length,  weight,  etc.  Under  either  of  these 
two  latter  interpretations  there  is  no  reason  why  we  should  regard  the  pro- 
IK)sitions  *B  =  C'  and  'A  =  B'  as  major  and  minor  premisses  respectively. 
Taken  together,  they  form  a  minor  premiss  for  use  with  the  major  premiss. 
'Things  which  are  equal  to  the  same  thing  are  equal  to  one  another.' 

Prof.  Groom  Robertson  long  ago  pointed  out  (Mind,  vol.  i.  p.  211) 
Jevons'  exaggerated  view  of  the  importance  of  these  'simple  identities,"  and 
the  confusion  which  follows  upon  his  attempt  to  distinguish  between  them 
and  equations  of  the  form  '  A  =  AB. '     If  the  sign  =  were  consistently  taken  to 


extremely  elementary  truth,  and  it  would  be  difficult 
to  find  the  exact  point  in  the  development  of  any 
young  child's  reasoning  powers  at  which  he  first  began 
to  take  it  for  granted,  though  unable  to  give  it  verbal 
expression  in  a  general  form.  It  is,  in  fact,  only  a 
corollary  from  our  instinctive  belief  in  causation, — 
from  our  belief,  that  is,  that  all  particular  cases 
come  under  general  rules.  Whether  expressed  or  not, 
and  whatever  phraseology  be  used  for  expressing  it, 
this  belief  is  part  of  the  constitution  of  any  mind 
that  forms  a  judgment  about  concrete  affairs.^  Not 
only  our  differences  of  creed  or  formula  but  even 
the  widest  possible  differences  of  belief  about  the 
ultimate  foundations  of  Nature  fail  to  affect  it ;  at 
most  they  affect  our  guesses  what  precisely  the  general 
rules  may  be.  For  instance,  some  people  hold  it  to 
be  a  trustworthy  general  rule  that  spirit-rapping  is 
nonsense,  or  that  sticks  cannot  be  chanojed  into 
serpents,  or  pumpkins  into  coaches,  while  others 
think  that  all  such  rules  need  qualification  to  allow 
for  wonders  and  miracles.  But  a  miracle  itself 
requires  for  every  mind,  however  unscientific,  some 
unity  behind  it, — some  law  under  which  it  takes  place, 
—  whether  this  be  conceived  as  a  hitherto  unknown 
law  of  Nature,  or  as  the  will  of  God,  or  as  the  pleasure 
of  fairies.     There   is   no   escape   from   the   abstract 

mean,  after  all,  the  same  as  the  old  copula  '  is,'  then  there  would  be  no  good 
rea.son  for  describing  as  '  equational '  any  syllogism  so  expressed,  and  they 
would  come  under  the  Aristotelian  conception  ;  if  on  the  other  hand  it  be 
taken  strictly  as  Jevons  claimed  to  intend  it,  then  it  covers  only  those  com- 
jtaratively  few  and  unimportant  reasonings  which  have  for  their  major  premiss 
the  axiom  above  quoted.  The  defects  of  this  axiom  when  it  is  extended  to 
take  in  similarity  (or  even  '  equivalence  ')  we  have  already  noticed  sufficiently 
in  §§  4  and  6. 

*  I  do  not  dispute  Prof.  Ward's  view  (XaturcUism  and  Agnosticism,  vol. 
ii.  p.  232)  that  there  would  be  no  absurdity  in  its  denial ;  but  that  does  not 
seem  to  carry  the  consequence  that  we  are  ever,  in  fact,  without  the  belief, 
nor  do  I  understand  him  to  mean  this. 


1 


74 


USE  OF  WORDS  IN  REASONING        pakt  i 


CH.  II,  §  14     REASONING  AND  SYLLOGISM 


75 


syllogistic  framework  iu  which  all  our  activity  of 
mind  i.s  confined  ;  however  far  we  develop  our  Logic 
we  cannot  outgrow  our  early  acceptance  of  the  axiom 
that  every  particular  case  has  a  general  rule  behind  it, 
and  the  corollary  that  proof  consists  in  finding  a 
general  rule  to  cover  the  particular  case.  The  effect 
of  our  efforts  to  make  our  Logic  more  scientific  is  not 
to  deny  this  elementary  truth  but  only  to  introduce 
more  care  in  its  application  to  given  arguments. 

If  Logic  had  no  particular  interest  in  disputed 
conclusions,  but  only  in  those  admitting  of  the  un- 
answerable demonstration  that  Euclid  irives,  we  might 
rest  satisfied  with  this  fundamentally  simple  account 
of  the  nature  of  reasoning.  We  are,  however,  inevi- 
tably led  beyond  it  if  we  are  asking  for  the  difi'erence 
between  good  and  bad  reasoning  not  only  in  cases 
where  every  one  can  see  the  defect  with  a  few  minutes' 
attention,  but  also  in  cases  where  doul)ts  persist  or 
recur,  where  strongly-held  views  confiict  with  each 
other,  and  where  accordingly  real  difficulties  have  to 
be  surmounted ;  those  questions,  in  short,  which  call 
for  something  more  intelligent  than  mere  mechanical 
rules  and  more  effective  than  rough  -  and  -  ready 
common  sense,  to  relieve  the  tension  or  to  clear  up 
some  of  the  fog.  From  this  point  of  view  the  syllo- 
gistic account  of  reasoning  is  interesting  mainly  as 
helping  to  show  the  point  at  which  the  more  subtle 
kinds  of  error  creep  into  an  argument, — namely  the 
middle  term.  The  conception  of  arguments  as  syl- 
logisms has  thus  an  entirely  different  function  from 
that  which  the  textbooks  would  lead  one  to  suppose. 
Instead  of  supplying  us  wuth  a  model  to  which  all 
our  arguments  ought  as  much  as  possible  to  conform, 
it  reminds  us  of  the  danijer  to  which  our  aroruments 


are  liable  just  in  proportion  to  their  appearance  of 
conforming  to  the  simple  syllogistic  type ;  what  we 
learn  by  means  of  it  is  how  to  find  the  vital  point 
of  an  argument,  the  point  at  which  to  look  for  the 
sources  of  possible  error,  especially  when  they  are 
difficult  to  find.  When  once  the  meaninor  of  the 
conclusion  is  agreed  upon,  then  the  only  possible 
fault  in  an  argument  is  that  of  an  over-simplified 
middle  ^  term,  a  middle  term  which  under  some  too 
concise  verbal  expression  obscures  the  real  complexity 
of  the  fact  relied  upon  as  sufficient  for  proof,  and 
thus  produces  an  ambiguity, — a  wandering  to  and 
fro  between  two  senses  in  which  that  term  may  be 
taken. 

We  see,  then,  why  the  attempt  to  force  all  argu- 
ments into  the  simple  syllogistic  mould  breaks  down. 
If  it  is  done  without  regard  to  possible  ambiguities 
of  the  middle  term,  then  the  misleading  power  of 
the  syllogistic  conception  is  great  in  proportion  to 
tlie  real  complication  and  difficulty  of  the  reasoning ; 
while  as  soon  as  Logic  does  begin  to  take  ambiguities 
into  account  the  simplicity  of  the  major  premiss 
disappears  in  a  cloud  of  fragments,  and  we  no 
longer  have  anything  resembling  a  simple  syllogism. 
The  syllogistic  conception  is  in  fact  only  applicable 
so  far  as  we  have  general  rules  which  can  be  absol- 
utely trusted ;  and  these  are  not  only  rare,  but  the 
few   that   there   are   belong   essentially   to   the   un- 

*  It  should  be  noticed  that  wliile  the  old  doctrine  of  the  Syllogism  gives 
no  more  than  a  formal  warning  against  ambiguity,  it  sometimes  (but  not 
always)  applies  this  warning  impartially  to  all  the  terms  in  the  syllogism 
and  not  to  the  middle  term  only.  This  is  no  doubt  due  to  its  pre-occupa- 
tion  with  the  problem  of  drawing  conclusions  from  given  premisses,  rather 
than  finding  jtremisses  for  a  given  conclusion.  (See  end  of  this  section.) 
hi  reflective  reasoning,  however,  we  start  from  the  conclusion,  having  first 
agreed  upon  its  meaning  ;  and  then  ambiguity  is  only  possible  in  the  middle 
term. 


76 


USE  OF  WORDS  IN  REASONING 


PART  I 


disputed  and  the  stagnant  parts  of  our  knowledge, 
like  the  propositions  of  Euclid  and  the  conclusion 
that  Socrates  is  mortal.  Wherever  knowledge  is 
growing — and  that  is  nearly  everywhere — it  does 
not  run  to  stringent  and  satisfactory  major  premisses 
but  to  glimpses  of  causation  seen  with  increasing 
insight  into  their  endless  complexity  of  detail. 

The  syllogistic  conception  may  also  be  of  use  in 
another  way.  It  is  often  worth  while  to  take  an 
argument  as  a  simple  syllogism  merely  for  the  pre- 
liminary purpose  of  discovering  what  general  views 
are  really  held  l)y  the  person  who  thinks  the  facts 
produced  are  sutlicient  to  prove  the  conclusion. 
The  nature  of  this  operation  may  best  be  seen  by 
contrasting  it  with  a  closely  similar  device  more 
commonly  used  in  disputation  ;  namely  w^here,  by 
taking  the  statement  of  fact  with  a  bare  literalness 
never  intended  by  the  assertor,  his  opponent  makes 
it  appear  to  involve  a  major  premiss  which  is  plainly 
absurd.  This  is  a  forensic  or  debating-society 
trick  of  a  rather  trivial  kind,  and  like  all  tricks 
it  argues  some  weakness  in  the  case  that  employs  it, 
but  an  example  of  it  may  help  to  remind  us  of  its 
commonness  and  to  show^  the  kind  of  effect  it  too 
often  produces.  The  following  ^  is  a  passage  said 
to  have  occurred  in  Lord  Erskine's  cross-examina- 
tion of  a  witness,  William  Hay,  in  the  trial  of  Lord 
Georfife  Gordon  : — 


The  witness  said  that  in  the  city  he  saw  *  the  very  siime 
man  carrying  the  very  same  flag  he  had  seen  in  the  fields.  He 
said  he  knew  it  was  the  same  man  because  '  he  looked  like  a 
brewer's  servant.'  *  Like  a  brru'rr\^  srrrant  /  What,  were  they 
not  all  in  their  Sunday  clothes  T     *0h,  yes,  they  were  all  in 

^  Quoted  from  Mr.  Baker's  Prim-iplcs  of  Argumentation. 


CH.  ii,Sl4     REASONING  AND  SYLLOGISM 


77 


their  Sunday  clothes.'  *  Was  the  man  with  the  flag  then  alone 
in  the  dress  of  his  trade  ? '  *  No.'  '  Then  how  do  you  know  he 
was  a  brewer's  servant  1 '  Poor  Mr.  Hay  !  ...  At  last,  after 
a  hesitation  which  everyl)ody  thought  would  have  ended  in  his 
running  out  of  court,  he  said  he  knew  him  to  be  a  brewer's 
servant  *  because  there  was  something  peculiar  in  the  cut  of 
his  coat,  the  cut  of  his  breeches,  and  the  cut  of  his  stockings  ! ' 
.  .  .  '  I  am  sure,  gentlemen,  you  will  not  forget,  whenever  you 
see  a  man  about  whose  apparel  there  is  anything  i^rcnliar,  to  set 
him  down  for  a  brewer's  servant.' 

Thoujih  this  instance  is  so  extreme  as  to  be  almost 
farcical,  it  serves  to  illustrate  the  way  in  which  the 
underlying  generalisation  may  be  unfairly  simplified 
till  it  becomes  absurd.  The  fact  that  there  is  *  some- 
thing peculiar'  about  a  man's  clothes, — or  even, 
more  particularly,  about  his  coat,  breeches,  and 
stockings, — is  obviously  not  sufficient  evidence  that 
he  is  a  brewer's  servant ;  and  yet  we  should  all 
admit  that  a  more  specified  peculiarity  of  dress 
mii^ht  be  sufficient,  and  that  the  fault  of  the  witness 
(supposing  him  honest)  probably  consisted  not  in 
his  assuminir  the  absurd  oreneralisation  which  is  here 
trickily  ascribed  to  him,  but  merely  in  his  failing  to 
specify  sufficiently  the  peculiarities  he  had  actually 
noticed.  There  is  nothing  absurd  in  using  peculi- 
arities of  dress  as  signs  in  this  manner,  and  nothing 
unusual  in  failing  to  give  a  clear  account  of  them 
afterwards.  We  can  often  distinguish  between  kinds 
of  things  that  are  nearly  alike — e.g.  between  English- 
men and  Americans  in  Paris — far  more  easily  than 
we  can  mention  precisely  the  points  of  difference 
seen.  Besides,  as  a  rule  we  fall  short  even  of  our 
own  best  power  of  description.  Through  hurry  or 
idleness,  or  through  the  wish  to  avoid  saying  un- 
necessary things,   our  account  of  a  fact  is  usually 


78 


USE  OF  WOEDS  IN  REASONING         part  i 


scantier  than  we  might  have  made  it ;  in  describing 
anything  we  habitually  take  some  risk  of  being  mis- 
understood.' 

The  legal  argument  just  quoted  certainly  has  the 
appearance  of  a  mere  rhetorical  trick.  But  the 
same  method  is  often  used  even  without  intentional 
sophistry,  and  then  we  can  only  suppose  that  the 
arguer  has  learnt  his  logic  from  the  textbooks  and 
has  failed  to  study  actual  arguments  with  intelligent 
observation  of  their  strength  and  weakness.  Sucli 
observation  does  not  indeed  put  an  end  to  the 
method  of  unduly  simplifying  the  generalisation,  yet 
wholly  transforms  its  character.  It  ceases  to  l>e  a 
trick,  and  becomes  a  useful  artifice.  It  ceases  to 
aim  at  a  closure,  and  merely  raises  a  further  inquiry, 
thus  becoming  one  of  the  chief  instruments  of  the 
fairest  possible  logic.  Instead  of  making,  witii  Lord 
Erskine,  a  triumphant  appeal  to  the  audience  to  find 
the  reasoning  absurd,  you  may  use  the  simplified 
generalisation  to  make  a  direct  appeal  to  the  witness 
to  attempt  a  further  specification  of  details  in  order 
to  explain  what  he  means.  Instead  of  considerincr 
the  inquiry  finished  and  the  conclusion  disproved, 
you  may  carry  the  inquiry  on  from  this  point  by 
assuming  that  the  tact  so  vaguely  and  baldly  stated 
{e.g.  "something  peculiar'')  is  really  a  more  relevant 
fact  than  it  seems  when  pinned  down  to  its  bare 
expression.       "  But  you   dont  mean  to  imply  that 


^  Where  De  Morgan  {Formal  Logu;  p.  20)  remarks  that  "tlie  honest 
witness  who  said,  '  I  always  thought  him  a  resiwctable  man, — he  kept  his 
gig,'  would  probably  not  have  admitted  in  direct  tenns  'every  man  who 
keeps  a  gig  must  be  resiiectable,'"  we  should  rather  say  that  the  witness 
would  probably  not  even  tacitly  imagine  that  any  such  rule  could  be  taken 
as  free  from  exce{)tions.  The  same  applies  to  another  example  quoted  by  De 
Morgan:  "his  imbecility  of  character  might  have  Inien  inferred  from  his 
proneness  to  favourites  ;   for  all  weak  princes  have  this  failing." 


CH.  H,  i^  14     REASONING  AND  SYLLOGISM 


79 


all  M  are  P"  is  a  common  form  into  which  this 
inquiry  runs,  its  purpose  being  to  force  a  clearer 
statement  of  what  the  implied  generalisations  really 
are.  Faulty  generalisations  are  often  forced  to  lose 
some  of  their  plausibility  in  becoming  less  vague  and 
tacit ;  but  even  where  no  such  result  follows  this  is 
usually  the  best  line  of  inquiry  if  you  wish  to  get  at 
the  speaker's  true  meaning,  and  so  to  approach  the 
question  how  far  a  stated  fact  is  sufficient  to  prove 
a  given  conclusion. 

The  task  of  finding  the  precise  generalisations 
which  are  involved  in  bringing  forward  a  fact  as 
relevant  is  nearly  always  difficult,  if  we  desire  to  do 
it  with  fairness.  It  is  difficult  even  to  know  them 
as  they  exist  in  our  own  minds,  and  naturally  still 
more  so  when  the  mind  that  entertains  them  is  not 
our  own,  and  we  have  only  another  person's  vague 
elliptical  statements  to  guide  us  in  the  search.  The 
search  for  them  is  necessarily  a  tentative  process.  No 
mechanical^  rule,  such  as  the  old  doctrine  of  the 
Syllogism  provides,  can  do  more  than  suggest  a  line 
of  inquiry ;  it  does  not  settle  the  question  except  in 
cases  so  simple  that  we  can  hardly  conceive  a  dispute 
arising.  The  aim  of  reflective  reasoning  is  to  trace 
doubts  and  difi'erences  of  opinion  to  their  source,  and 
the  more  simple  and  straightforward  we  assume 
this  difficult  problem  to  be,  the  more  crude  and 
unsatisfactory  will  be  our  eff'orts  to  solve  it.  For  if 
an  argument  is  really  simple,  then  common  sense  is 

*  The  truly  mechanical  nature  of  the  Syllogism  when  sentence  and  asser- 
tion are  confused  is  evident  from  the  fact  that  Jevons  constructed  a  wooden 
machine  for  getting  conclusions  from  premisses  with  perfect  accuracy.  We 
need  not  go  so  far  as  to  say,  in  Mr.  Spencer's  words  {Principles  of  Psychology, 
vol.  ii.  p.  90)  that  such  processes  have  "  nothing  to  do  with  thought  at  all," 
but  at  any  rate  they  have  little  to  do  with  subtle  errors  in  reflective  reason- 
ing.    The  only  complexity  they  deal  with  is  of  an  open  and  innocent  kind. 


1 


80 


USE  OF  WORDS  IN  REASONIXG         part  i 


bufticieiit  for  the  occasion  and  careful  Logic  is  not 
called  for,  while  if  it  is  only  apparently  simple  it  is 
even  more  deceitful  than  where  its  complexity  stares 
us  in  the  face.  That  is  the  dilemma :  the  appear- 
ance of  simplicity  cannot  he  trusted,  and  real 
simplicity  (so  far  as  such  a  thing  can  be  said  to 
exist)  is  only  evidenced  by  the  absence  of  dispute. 
So  long  as  every  one  agrees  about  a  given  con- 
clusion there  is  no  more  to  be  said  about  it,  but 
the  moment  dispute  arises  we  have  a  case  where  one 
party  suspects  the  other  of  having  been  deceived  by 
a  false  simplicity  in  the  middle  term. 

As  regards  the  use  of  the  Syllogism  not  for 
reflective  proof  of  a  disputed  conclusion,  but  for 
putting  together  given  propositions  as  premisses  and 
so  reaching  a  new  conclusion,  that  is  of  small  import- 
ance except  as  providing  exercises  in  Formal  and 
Symbolic  Logic.  Faults  in  the  'reasoning  process' 
so  conceived  belong,  as  we  found  in  §  3,  rather  to  the 
grammatical  than  the  logical  aspect  of  the  syllogism  ; 
and  the  occasions  on  which  we  get  premisses  before 
we  have  an  inkling  of  the  conclusion  are,  besides, 
neither  so  frequent  as  Formal  Logic  supposes  nor  of 
a   kind  to  conceal  difficulty  and  so  create  effective 


error. 


1 


§15. — Summary  of  thk  Chapter 

In  this  chapter  we  have  been  solely  occupied 
with  the  nature  of  reflective  reasoning  and  with  the 
kind  of  objections,  and  replies  to  objections,  that 
constitute  the  framework  of  every  argument  about 
a  proposed  conclusion.  We  saw  that  the  position 
of  the  objector  to  a  conclusion  is  better  conceived  in 

1  For  furthtT  remarks  on  this  i»oiut,  see  §  62. 


•■I 
■4 


CH.  n,§15     REASONING  AND  SYLLOGISM  81 

general  as  that  of  an  inquirer  than  a  scoffer,  though 
there  usually  comes  a  point — too  soon,  if  we  are 
shallow  logicians — where  our  inquiry  is  satisfied  and 
we  accept  or  reject  the  conclusion  on  its  apparent 
merits.  Reflective  reasoning,  we  found,  is  the  pro- 
duction of  '  facts '  as  sufficient  to  support  conclu- 
sions, the  sutKciency  being  made  up  partly  of  the 
truth  of  the  facts  produced,  and  partly  of  their 
relevance ;  and  we  saw,  further,  that  to  recognise  the 
relevance  of  a  fact  is  the  same  thing  as  to  recognise 
the  truth  of  a  general  principle — a  theory  about  the 
way  in  which  certain  facts  are  connected  by  natural 
law — so  that  any  defects  in  our  implied  theories  are 
at  the  same  time  defects  in  the  relevance  of  our  facts  ; 
defects  which,  of  course,  may  or  may  not  turn  out 
on  inquiry  to  be  important. 

Then  we  noticed  how  it  is  that  these  two  ele- 
ments in  proof  correspond  exactly  to  the  two  pre- 
misses in  the  ancient  conception  of  Syllogism ;  which 
conception,  when  it  is  freed  from  the  dust  raised 
by  confusing  sentences  with  assertions,  stands  out 
clearly  as  our  recognition  of  law  in  Nature,  our 
recognition  that  all  particular  cases  come  under 
general  rules,  and  that  consequently  our  reflective 
assurance  that  we  understand  correctly  any  particular 
case  (the  conclusion)  depends  on  our  power  of  fitting 
it,  by  means  of  a  minor  premiss,  to  the  general  rule 
to  which  it  properly  Ijelongs.  But  we  found  two 
important  difficulties  in  applying  this  conception  to 
cases  of  argument,  first,  that  in  many  cases  there  is 
evident  complexity  in  the  fact  produced,  necessitating 
a  corresponding  complexity  in  the  major  premiss, 
oiten  sufficient  to  prevent  such  major  premiss  from 
appearing   any   better   known   than    the    conclusion 


4 


82 


USE  OF  WORDS  IN  REASONING        part  i 


itself;  and  secoiidly,  that  even  where  there  is  an 
appearance  of  simplicity,  and  where  accordingly  we 
tend  to  view  the  process  as  syllogistic,  the  appear- 
ance may  very  well  be  deceptive, — the  premisses  may 
seem  to  be  connected  by  the  middle  term  and  yet 
the  connection  may  be  faulty  and  the  reasoning 
therefore  false.  Since  these  are  the  cases  in  which 
the  error  is  most  concealed  they  are  of  special  interest 
to  Logic. 

A  syllogism  used  for  proof,  then,  is  a  judgment 
(the  conclusion)  expanded  so  that  the  two  disputable 
elements  in  it  shall  lie  open  to  inspection.  In  a 
reflective  syllogism  the  premisses  Iiave  no  priority  to 
the  conclusion,  but  rather  come  out  of  it.  And  this 
view  materially  alters  the  notion  of  j)roof  as  popularly 
conceived.  Following  the  old  superstition,  strict 
proof  is  popularly  supposed  to  be  '  mathematical 
demonstration ' ;  and  the  defender  of  a  shaky  theory 
may  still  be  found  admitting  with  apparent  candour 
that  to  supply  mathematical  demonstration  of  it  is 
beyond  his  power.  But  in  the  light  of  the  above 
account  of  the  Syllogism  such  an  admission  becomes 
irrelevant ;  for  the  most  that  any  proof  can  do,  in  the 
case  of  disputed  conclusions,  is  to  challenge  the 
objector  to  find  definite  fiiult  with  the  reasons  given 
for  belief.  Sometimes  the  obvious  fault  is  that  a 
major  premiss  is  wanting,  sometimes  that  the  minor 
premiss  is  untrue ;  but  even  where  an  apparently 
faultless  syllogism  is  produced  it  is  still  quite  possible 
that  the  middle  term  sufters  from  ambiguity.  To  oft'er 
proof  is  to  offer  definite  points  of  attack,  and  there 
are  many  conclusions — in  fact  most  of  those  which 
are  worth  discussing  at  all — where  anything  resem- 
bling  mathematical    demonstration    would   have    an 


CH.  n,.U6     REASONING  AND  SYLLOGISM  83 

effect  as  far  removed  as  possible  from  being  satisfac- 
tory. It  would  make  the  objector  feel  sure  that 
there  must  be  some  ambiguity  if  he  could  only  find 
it.  When  matters  of  real  doubt  and  dispute  arise, 
and  continue,  between  any  two  parties  of  average 
men,  it  is  extremely  unlikely  that  a  perfectly  un- 
ambiguous syllogism  can  be  found  to  support  either 
side.  Complex  and  difficult  (questions  are  not  to  be 
settled  by  merely  guarding  against  the  formal  errors 
of  demonstration.  Any  general  rules  laid  down  for 
the  purpose  are  of  necessity  simple  and  obvious — 
except  for  their  technical  dress — and  to  suppose  that 
our  neighbours  break  them  only  through  sheer  ignor- 
ance or  carelessness  is  just  the  kind  of  pharisaical 
assumption  that  can  only  keep  Logic  in  evil  repute. 
It  is  not  the  abstract  principles  of  correct  reasoning 
that  are  unfamiliar  to  the  average  man  (except  in 
their  technical  expression)  but  the  limits  of  the  safe 
application  of  those  principles  when  the  concrete 
sul)ject-matter  is  taken  into  account. 

It  should  now  begin  to  be  a  little  clearer  what 
is  meant  by  saying  that  ambiguity  of  the  middle 
term  of  a  syllogism  is  the  root  of  all  the  most 
important  kind  of  error  in  reflective  reasoning.  That 
statement  is  as  far  as  possible  from  implying  that 
arguments  in  general  are  best  conceived  as  simple 
syllogisms.  Indeed  it  reminds  us  that  so  to  con- 
ceive any  argument  is  precisely  to  ignore  the  risk 
of  such  ambiguity.  The  decision  how  far  it  can 
safely  be  ignored  in  a  given  case  is  one  of  the 
eternal  difficulties  in  forming  judgments  correctly, 
as  we  shall  see  more  in  detail  in  Part  IL  But 
already  we  have  got  some  glimpses  of  the  nature 
and  effects  of  ambiguity.     Though  we  have  left  the 


84 


USE  OF  WORDS  IN  REASONING 


PARTI 


question  open  whether  all  statement  of  fact  is  over- 
simplified, we  have  seen  the  manner  in  which  a  false 
simplicity  may  on  occasion  be  given  to  a  fact  hy 
means  of  a  general  name,  and  that  whenever  this 
is  the  case  the  remedy  lies  in  brin^jing  to  light  more 
of  the  details  that  are  covered  by  the  wide  and 
vague  expression.  In  the  hiding  of  these  details  the 
ambiguity  of  the  middle  term  always  consists.  And 
in  thus  expanding  the  minor  premiss  we  necessarily 
expand  the  major  premiss  also,  until  the  attempt  to 
regard  it  as  a  single  simple  generalisation  of  the 
type  *'  All  men  are  mortal  "  becomes  impracticable 
or  useless.  The  further  we  push  the  inquiry  what 
details  are  comprised  in  the  fact  produced  as  relevant, 
the  more  we  find  that  the  argument  involves  rather  a 
cluster  of  generalisations  than  a  single  major  premiss, 
and  that  the  task  of  judging  its  value  resolves  itself 
into  separating  these  into  better  and  worse  ones,  and 
getting  the  worse  ones  corrected.  Indeed,  if  we 
leave  the  simplest  and  least  interesting  cases  of 
argument  out  of  account,  it  is  easy  to  see  that 
(when  once  the  issue  is  clear)  the  whole  process,  as 
between  two  persons  arguing,  is  a  search  on  the 
part  of  each  for  false  views  held  by  the  other  as 
to  the  way  in  which  certain  things  are  connected  in 
the  ordinary  course  of  Nature.  The  personal  aim 
in  every  disputed  question  of  fact  is  to  show  that 
your  opponent's  general  knowledge  is  somehow  de- 
fective ;  and  the  direct  ostensible  object  is  to  show 
that  in  consequence  of  his  ignorance  he  has  reached 
a  false  conclusion  in  the  particular  case.  The 
objector  accuses  the  assertor,  in  effect,  of  being 
misled  by  appearances,  or  by  words, — and  thus  of 
conceiving  either  his  facts  or  his  causal   rules  too 


CH.  n,  §  15     REASONING  AND  SYLLOGISM 


85 


simply.  Tlie  assertor  acciuses  the  objector  of  making 
too  much  of  some  small  difference  which  is  better 
left  unnoticed.  Between  them  who  is  to  judge  ? 
Not  Logic,  certainly,  or  at  least  not  Logic  alone  but 
Logic  and  special  knowledge  together.  For  this 
reason  any  mechanical  logical  rules  foi*  decdding  the 
rights  of  an  argument  without  regard  to  its  subject- 
matter  are  of  necessity  futile.  The  function  of 
Logic  is  not  to  judge  which  reasoned  views  about  a 
matter  of  fact  are  best,  but  merely  to  establish  a 
method  for  pursuing  that  elusive  question  in  the 
fairest  and  most  effective  manner. 


4 


CHAPTER  III 

REASONING   AND   GENERALISATION 

§  If). — Hypothesis  depends  on  Previous 

Theory 

At  several  points  in  the  preceding  chapter  the 
dependence  of  judgment  upon  previously  -  formed 
judgment,  and  especially  upon  previously  -  formed 
generalisations  about  the  course  of  Nature,  came  into 
view.  We  saw,  for  instance,  that  all  recognition  of 
the  relevance  of  a  fact  towards  the  proof  of  a  given 
conclusion  is  nothing  else  than  the  recognition  of 
such  generalisations ;  that  it  is  these  which  enaljle  us 
to  '  take  facts  for  what  they  are  worth,'  and  which 
limit  and  guide  our  analysis  of  facts  into  their  im- 
portant and  unimportant  details.  We  noticed  too 
that  disputed  questions,  when  the  dispute  is  carried 
far,  depend  rather  on  differences  of  view  about  the 
causes  and  effects  of  things  than  upon  anything 
simpler.  A  dispute,  for  instance,  as  to  whether  a 
certain  event  happened  or  not  is  of  a  more  resolv- 
able nature,  and  comes  sooner  to  an  end,  than  a 
dispute  as  to  hoiv  it  happened  and  what  it  really 
involved  or  involves.  So  far  as  questions  of  fact 
can  be  distinguished  from  other  questions,^  the  former 

»   As  to  til  is  ditiiculty,  see  §  49. 


I 

I 


r».  ni,§16  REASONING  AND  GENERALISATION    87 

have  less  controversial  importance.  Where  verifica- 
tion is  easy,  difference  of  opinion  flags  for  lack  of 
material ;  theory,  as  such,  is  the  vital  point  of  disputes. 

Accordingly  Logic  has  considerable  interest  in  the 
(question  how  our  major  premisses  —  or  our  frag- 
mentary glimpses  of  causation — are  arrived  at.  But 
about  this  question  the  first  thing  to  notice  is  its 
unnecessary  vagueness  as  thus  stated.  There  is  an 
important  difference  between  the  question  how  the 
first  of  our  generalisations  came  into  existence  and 
the  question  how  an  existing  store  of  them  grows 
and  develops  ;  and  it  is  advisable  to  postpone  any 
curiosity  about  the  former  problem  until  we  have 
exhausted  all  the  answeraV)le  questions  in  the  world. 
For  since  we  are  without  experience  of  a  mind 
wholly  ignorant  of  the  ways  of  Nature  there  is 
iiotliing  to  check  or  to  verify  our  guesses  about  the 
workings  of  such  a  mind.  It  is  difficult  to  put  our- 
selves at  the  point  of  view  even  of  a  dog  with  any 
assurance  of  success ;  how  much  more  difficult  must 
it  be  to  imaorine  the  state  of  a  mind  in  which  the 
conception  of  order  in  Nature  has  not  yet  begun. 
For  this  reason  we  shall  here  consider,  not  how 
the  earliest  generalisations  of  all  were  formed  out 
of  something  not  yet  generalisation,  but  how  they 
are  formed  in  a  mind  which  already  possesses  a  store 
of  general  knowledge  or  beliefs.  How  does  the  man 
of  to-day,  or  of  any  historical  times,  increase  his 
experience  of  the  ways  of  Nature  ? 

The  process,  where  any  care  ^  is  used,  consists  of 

'  We  may  pass  over  the  question  whether  generalisations  are  ever 
formed  wlwlly  without  care,  or  by  'simple  enumeration.*  If  there  be 
any  such  cases  the  theory  of  careful  inference  has  no  concern  with  them. 
The  two  stages  here  sjwken  of  are  at  any  rate  discoverable  at  a  very  low 
level  of  common-sense  inquiry  into  the  way  things  happen. 


s 


88 


USE  OF   WORDS  IN  REASONING        part  i 


two   stages, — guessing  and  verification.      A  certain 
theory  of  the  connection  between  X  and  Y  is  pro- 
posed   as   a    liypothesis,    and    then    we    proceed    to 
examine  how  far   it  squares    with  the   ascertainable 
facts.       This    does    not    mean,    of   course,  that    the 
division  into  two    stages    is   always  sharp  or  rigid, 
or  that  it  is  ever  final ;  but  only  that  these  are  the 
two  distinguishable  elements  of  the  process,   how- 
ever much  they  may  be  repeated  or  entangled.     A 
first  hypothesis,  for  instance,  is  often  discredited  by 
a   first    attempt    at    verification,    and   this    in    turn 
suggests    a    slightly    altered    hypothesis    wliicth    on 
further   appeal    to   the    facts   turns   out    to   recjuire 
still  further  modification.       We   be<^in  bv  observing' 
that  X   and   Y — e.g.  hailstorms    and    thunder — are 
found  in    more  or  less   close  connection  with    each 
other,  and  we  guess  that  they  somehow   belong  to- 
gether in   the    regular    course  of  Nature.      In  seek- 
ing to  do  away  with  the  vagueness  of  that  'some- 
how,'   and    to    express   the    law    in    definite    terms, 
various    well-known  operations   are    connnonly    per- 
formed,— such    as    observing   carefully   or  minutely, 
collecting   a    large   number   of   observations,    tryin<r 
experiments  under  control,  or  repeating  experiments 
using  more  and  more  control  over  the  circumstances, 
till  we  think  we  have  eliminated  as  many  sources  of 
error  as  we  need  consider.     And  wherever  we  choose 
to   stop   this  process  of  verification   of  guesses,    we 
have  got  an  inductive  'conclusion,'  —  for  what  it  is 
worth.     If  there  are  any  generalisations  which  leave 
no   room   for  increased   accuracy  of  conception   and 
statement,  due  to  increased  acquaintance  with  facts, 
it  is  hardly  in  the  name  of  scientific  Logic  that  we 
can  pretend   to    know   which  exactly   these    perfect 


CH.  ni,^17  REASONING  AND  GENERALISATION  89 

generalisations  are.  Indeed,  when  we  leave  out  of 
account  the  few  cases  where  it  is  at  present  most 
uncertain  whether  any  fault  will  eventually  be  found, 
it  is  remarkable  how  easy  it  is  to  show  of  most  of 
our  ordinary  generalisations  that  they  will  bear 
further  refinement. 


§  17. — Verification  also  depknds  on 
Previous  Theory 

No  one  disputes  the  fact  that  our  previous  general 
knowledge  of  Nature  is  the  only  source  of  our  guesses, 
but  that  it  is  also  a  chief  determining:  factor  in  veri- 
fication  is  rather  less  obvious,  and  its  effects  are  often 
overlooked.  Verification  takes  place  by  means  of  "  \ 
methods  such  tis  those  which  were  formulated  by 
Mill  and  are  now  duly  reiterated  in  all  the  text- 
books which  deal  with  '  inductive  Logic,'  but  there 
are  certain  ways  in  which  the  usual  account  of  them 
is  misleading.  A  minor  point  is  as  to  the  number  of 
distinct  and  separate  methods  which  should  be  recog- 
nised. Herschel,  whose  view  of  induction  seems  to 
have  greatly  influenced  Mill,  distinguished  no  less 
than  nine  ''rules  of  philosophizing."^  Mill  reduced 
the  number,  but  it  is  not  quite  clear  whether  in  his 
view  they  may  best  be  regarded  as  five,  or  four,  or 
two,  or  one ;  for  he  lays  down  five  separate  canons, 
heads  the  chapter'^  "The  Four  Experimental  Methods," 
and  yet  acknowledges  that  the  Method  of  Agreement 
and  the  Method  of  Difference  are  fundamental,  the 
others  being  mere  variations  of  them  due  to  special 
circumstances  of  the  inquiry.     Finally,  since  he  says  ^ 

*   Disrourse  on  the  Study  of  Natural  Philosophy,  §§  145-158. 

2  System  of  Logic,  book  iii.  chap.  8, 

3  Ibicl.,  §  3. 


90 


USE  OF  WORDS  IN  REASONING        part  i 


that  the  Method  of  Difference  "  is  more  particularly 
a  method  of  artificial  experiment,  while  that  of  Agree- 
ment is  more  especially  the  resource  employed  where 
experimentation  is  impossible,"  and  that  **  it  is  by  the 
Method  of  Difference  alone  that  we  can  ever,  in  the 
way  of  direct  experience,  arrive  with  certainty  at 
causes,"  there  is  some  ground  for  holding  that  Mill 
in  fact  recognised  no  more  than  one  fundamental 
method,  with  four  inferior  substitutes  to  be  used 
where  the  circumstances  allow  of  nothins:  better.  If 
we  once  begin  to  take  awkwardness  of  circumstances 
as  creating  separate  methods,  where  is  an  end  to  be 
found  to  the  number  ?  If  difference  of  circumstances 
involves  difference  of  method,  then  we  should  have 
to  admit  that  every  worker  in  every  branch  of  science 
uses  special  methods  of  his  own.^ 

The  unity  of  inductive  method  would  perhaps 
have  been  still  more  apparent  to  Mill  if  he  had  con- 
sistently seen  that  his  Method  of  Agreement  and  his 
Method  of  Difference  cannot  well  be  conceived  as  two 
separate  ways  of  attacking  the  same  problem,  but  are 
rather  statements — misleadingly  abstract  statements, 
but  let  that  pass  for  a  moment — of  what  is  required 
for  the  verification  of  a  theory  at  two  different  stages 
of  its  growth.     Under  this  aspect  of  them   the  kind 

>  It  may  also  be  remarked  that  the  names  '  Method  of  Agreement '  and 
'  Method  of  Difference '  are  not  quite  happily  chosen,  for  the  reason  that 
each  of  them  equally  requires  both  agreement  and  difference  in  the  circum- 
stances observed.  The  essence  of  the  so-called  Method  of  Agreement  is 
that  two  or  more  cases  which  agree  in  exhibiting  the  conjunction  of  X  with 
V  should  also  differ  in  as  many  other  respects  as  jiossible  ;  for  if  they  do 
not  differ  sufficiently,  the  inference  tends  to  be  by  'simple  enumeration.' 
Similarly  the  essence  of  the  Method  of  Difference  is  that  the  cases  observed 
should  agree  in  all  but  the  presence  of  X  ;  or  else  the  argument  tends  to  be 
merely  *  post  hoc,  ergo  propter  hoc. '  Though  the  first  methoti  relies  upon 
agreement  in  the  midst  of  difference,  while  the  second  relies  uj)on  difference 
in  the  midst  of  agreement,  in  both  alike  every  point  of  agreement  and 
every  point  of  difference  must  be  observed  with  as  much  care  as  the  case 
requires. 


CH.  iii,§17  REASONING  AND  GENERALISATION  91 

of  problem  supposed  to  be  answered  by  using  the 
Method  of  Agreement  is  whether  the  conjunction  of 
X  with  Y  is  (approximately)  universal ;  whereas  the 
Method  of  Difference  is  supposed  to  tell  us  whether 
some  particular  observed  event  has  been  correctly 
analysed  into  cause  and  effect.  What  probably  led 
Mill  to  overlook,  at  times,  the  difference  between  these 
two  inquiries  was  the  reflection  that  a  generalisation  is 
'  merely  empirical '  until  w^e  can  see  causation  behind 
it ;  hence  a  generalisation  of  the  form  'All  X  are  Y  ' 
must  be  broken  up  into  generalisations  of  the  form 

*  A  causes  a '  ^  before  it  has  a  right  to  be  called  an 
indui^tion  in  the  stricter  sense.  And  it  is  quite  true 
that  (since  the  same  cause  always  has  the  same  efiect) 
the  inquiry  whether  A  in  general  causes  a  cannot 
be  distinguished  clearly  from  the  inquiry  whether  A 
(lid  cause  a  in  any  observed  occurrence  in  w^hich  A 
and  a  are  found  in  succession.  Still,  it  is  also  true 
that  investigations  which  afterwards  develop  into 
detailed  questions  about  strictly  uniform  succession 
between  A  and  a  normally  begin  with  the  vaguer 
problem  whether  X  and  Y  are  connected  otherwise 
than  accidentally  ;  and  that  for  attacking  this  vaguer 
problem  the  plan  of  singling  out  agreement  in  the 
midst  of  difference  is  often  more  suitable  than  that 
of  singliug  out  difference  in  the  midst  of  agreement.'^ 

However,  we  all  agree  that,  where  the  problem  is 
to  verify  the  guess  that  A  is  connected  with  a  by 

*  direct '  causation,  the  only  method  consists  in  analys- 

*  I  here  adoi)t  Mill's  symbols,  in  spite  of  their  obvious  defect.  There 
seems  to  be  no  way  of  expressing  in  letters  a  supposed  cause  and  a  supposed 
effect  without  emphasising  either  the  connection  or  the  disconnection 
unduly. 

'  Mill  came  near  seeing  this  when  he  said  (8th  edition,  vol.  i.  p.  455), 
••The  Method  of  Agreement  is  chiefly  to  be  resorted  to  as  a  means  of  suggest- 
ing applications  of  the  Method  of  Difference." 


92 


USE  OF  WORDS  L\  REASONING        part  i 


iiig  one  or  more  observed  occurrences  until  we  are 
satisfied  that  errors  have  l)een  sufficiently  provided 
for.  The  best  way  of  doing  this — where  it  is  possible 
— is  to  introduce  the  factor  A  into  a  known  set  of 
circumstances,  BCD,  and  then  see  what  happens. 
If  a  appears,  we  argue  very  naturally  that  this  change 
(assuming  it  to  be  the  only  change  observable)  was 
directly  due  to  the  prior  change  we  made  in  the 
circumstances.  But  often,  as  Mill  recognised,  we 
have  to  put  up  with  less  conclusive  evidence,  whether 
we  do  or  do  not  dignify  these  second-best  operations 
with  the  name  of  inductive  methods.  If  we  cannot 
use  the  direct  Method  of  Ditference  we  use  tlie 
nearest  approat^h  to  it  that  circumstances  will  allow. 

Now  the  defects  of  the  second-best  methods  lie 
mostly  on  the  surface,  and  are  admitted,  I  believe,  by 
all  exjjounders  of  them,  including  certainly  Mill 
himself.  As  he  carefully  explains,  they  are  onlv 
approximations  to  the  Method  of  Difference,  and  their 
value  depends  on  their  approximation  to  it.  But 
what  Mill  did  not  clearly  see,  and  what  the  usual 
exposition  in  the  textbooks  also  tends  to  overlook, 
is  that  even  the  Method  of  Difference  is  (so  to  speak) 
only  an  approximation  to  itself  That  is  to  say, 
there  is  a  difference  between  any  attempt  to  apply 
the  method  in  the  concrete  and  the  method  itself  as  an 
abstract  ideal ;  we  never  have  any  guarantee,  except 
so  far  as  our  incomplete  store  of  general  knowledge 
can  give  us  one,  that  an  apparent  application  of  the 
Method  of  Difference  really  fulfils  the  stringent  con- 
ditions required  by  it.  In  the  abstract  no  fault  can 
be  found  with  the  rule,  but  it  is  always  in  concrete 
cases  that  any  rule  must  be  applied,  and  nothing  is 
easier  than   to  apply  it  wrongly.      Regarded  as  an 


CH.iii,§17  REASONING  AND  GENERALISATION   93 

applicable  rule  it  does  not  show  us  how  to  reach  true 
inductions,  but  merely  expresses  the  aim  wx  have 
always  had  in  view  whether  the  inductions  actuallv 
reached  are  true  or  false.  What  is  insufficiently 
dwelt  on  in  the  usual  formal  account  of  the  method 
is  that  the  guarantee  of  correctness  is  not  to  be  found 
in  the  Method  of  Difference  itself,  but  in  the  wisdom 
and  care  with  w^hich  we  apply  it, — wisdom  previously 
gathered  and  care  w^hich  is  objectless  except  through 
our  past  experience  of  the  possible  risks  of  error. 
Even  in  the  best  and  most  recent  textbooks^  this 
point  is  somewhat  scantily  treated,  w^hile  in  others 
whi('h  are  still  widely  used  -  no  reference  is  made  to  it, 
and  the  account  that  is  given  leaves  the  student  under 
the  impression  that  the  value  of  a  given  experiment 
consists  in  its  appearayice  of  fulfilling  the  ideal  of 
the  Method  of  Difference,  rather  than  in  the  sound- 
ness of  our  judgment  (external  and  prior  to  the 
application  of  the  method)  that  this  appearance  is 
not  in  the  given  case  deceptive, — as  it  is,  for  instance, 
in  every  successful  conjuring  trick,  and  in  every  experi- 
ment by  which  science  is  in  the  smallest  degree  misled. 
The  weak  point  of  the  rule  ^  that  is  laid  down  by 
the  Canon  of  the  Method  of  Difference  is  to  be  found 


'  See  for  instance  Mr.  Carveth  Read's  Loijii\  Deductive  and  Inductice,  di>. 
180-183.  ^^ 

'  E.g.  Jevons's  E/cnuiitunj  Lessons,  xxviii. 

^  This  rule  or  *  canon '  was  stated  by  Mill  as  follows:  —  "If  an 
instance  in  which  the  phenomenon  under  investigation  occurs,  and  an 
instance  in  which  it  does  not  occur,  have  every  circumstance  in  common 
save  one,  that  one  occurring  only  in  the  former  ;  the  circumstance  in  which 
alone  the  two  instances  ditfer  is  the  effect,  or  the  cause,  or  an  indispensable 
i>art  of  the  cause,  of  the  phenomenon."  The  wording  of  the  rule  is  some- 
what obscure,  but  Mill's  illustration  of  it  removes  all  the  vagueness  except 
as  to  what  may  be  meant  by  a  '  single '  circumstance.  What  is  required, 
Mill  says,  is  a  double  set  of  instances,  ABC  becoming  ahc,  and  BC  becoming 
be ;  this  is  supjwsed  to  prove  that  A  causes  a  ;  and,  no  doubt,  would  prove  it 
it  we  could  be  sure  of  the  singleness  of  the  circumstance  called  by  the  single 
name  A.  jo 


94 


USE  OF  WORDS  IN  REASONING         part  i 


in  its  glib  use  of  phrases  like  *  every  circumstance 
save  one,'  and  *  the  circumstance  in  wliich  alotte 
the  two  instances  differ.'  All  talk  ahuul  'single 
circumstances'  is  loose  talk,  and  the  fact  that  any 
mistakes  are  ever  made  in  attributing  given  effects  to 
particular  causes  is  itself  a  sign  that  it  is  possible  to 
take  for  a  sinirle  circumstance  some  <ircumstance 
which  is  not  single  but  complex,  indeed,  if  we  think 
of  it,  there  can  be  no  other  source  of  false  causal  ex- 
planation. This  is  most  easily  seen  in  cases  where 
the  fault  does  not  involve  a  great  amount  of  careless- 
ness. When  we  have  l^egun  to  get  beyond  the  savage 
method  of  merely  singling  out  any  striking  antecedent 
circumstance  (such  as  the  appearance  of  a  comet)  and 
any  striking  consequent  circumstance  (such  as  a  defeat 
or  a  pestilence),  and  connecting  the  two  as  cause  and 
effect  with  a  minimum  of  reflection, — when  we  have 
begun  at  all  to  collect  and  compare  instances,  and  to 
make  experiments, — then  our  fault,  if  the  inference 
is  faulty,  evidently  consists  in  our  having  made  an  in- 
sufficient analysis  of  the  circumstances.  The  '  single 
circumstance '  A,  which  we  added  to  the  set  of  cir- 
cumstances BCD,  is  (whenever  our  inference  is  false) 
not  really  single,  but  is  a  mixture  of  circumstances 
some  of  which  are  essential  to  a's  occurrence  and 
others  not  so ;  and  the  name  A,  applied  indiscrimi- 
nately to  the  whole  of  them,  emphasises  the  wTong 
set  of  the  component  circumstances.^  In  performing 
this  operation  we  have  tried  to  use  the  Method  of 
Difference,  but  we  have  applied  it  wrongly  because 
our  facts  were  wrongly  conceived.     All  careful  ex- 

*  A  striking  instance,  too  long  to  quote  here,  is  given  in  ray  book  The 
Process  of  Argument,  pp.  95-97.  h\  the  same  way  the  complex  fact  which 
consists  partly  of  prayer  and  partly  of  keeping  your  powder  dry  may  easily 
have  one  of  these  two  component  details  over-emphasised. 


CH.  ni,U8  REASONING  AND  GENERALISATION  95 

planation  of  an  occurrence  as  causal  involves  the  use 
of  the  Method  of  Difference  or  one  of  the  makeshift 
methods  which  aim  at  the  same  result ;  but  precisely 
because,  owing  to  mistakes  of  fact,  we  can  apply  them 
wrongly,  error  is  possible,— and  frequent.  We  may 
always  fancy  a  named  circumstance  single,  but  we 
can  never  be  sure  that  it  is  single,  or  that  the 
name  A  is  not  misleading  in  this  context,  until  we 
are  sure  that  our  inductive  inference  is  free  from 
error.  So  that  to  put  forward  our  use  of  these 
axioms  as  any  test  of  the  correctness  of  our  inference 
is  to  put  the  cart  before  the  horse. 


§  18. — Use  of  the  Inductive  Methods 

We  may  here  ask,  regarding  the  inductive  methods, 
as  we  asked  in  last  chapter  about  the  Syllogism, 
whether  this  criticism  is  intended  to  condemn  them 
entirely.  And  again  it  can  be  freely  admitted  that 
something  less  than  total  condemnation  is  sufficient. 
Just  as  in  the  case  of  the  syllogistic  conception  so  in 
the  case  of  the  Method  of  Difference,  the  mischief 
only  begins  with  the  assumption  that  the  fact  of 
using  it  {i.e.  of  intending  to  use  it,  and  thinking  we 
have  done  so)  can  by  itself  give  anything  like  what 
Miir  called  *  rigorous  certainty.'  It  is  true  that 
Mill  seems  to  have  been  at  other  times  aware  of 
difficulties  in  applying  the  method,  and  that  various 
later  writers  ^  have  discussed  these  difficulties  at  con- 
siderable length.  Yet  there  is  room,  I  think,  for 
further   attempts   to   bring  before   the   student   the 

*  Vol.  i.  p.  459.  On  the  same  page  he  speaks  of  it  as  an  "infallible 
method." 

2  For  a  purely  hostile  account  see  Mr.  Bradley's  Principles  of  Logic,  book 
ii.  part  ii.  chap.  iii.  Dr.  Venn's  more  sympathetic  treatment  of  the  question 
{Empirical  Logic,  chap,  xvii.)  is  naturally  fuller  of  useful  suggestions. 


96 


USE  OF  WORDS  IN  REASONIXC 


PARTI 


fact  that  an  inductive  conclusion  does  not  get  its 
value  from  the  mere  use  of  any  inductive  method, 
hut  from  a  quality  which  in  varying  strength  accom- 
panies such  use.  Whatever  name  we  may  give  to 
that  quality, — care,  or  discretion,  or  insight,  or 
scientific  genius, — its  effectiveness  on  a  given  occasion 
is  limited  by  our  previous  knowledge  hearing  on  the 
point ;  and  this  is  indeed  the  only  explanation  of  the 
extraordinary  scientific  errors  (as  they  now  seem)  com- 
mitted by  the  intellectual  giants  of  former  times.  No 
doubt  they  knew,  in  the  abstract,  what  was  wanted 
for  proof,  as  well  as  the  most  modern  inquirer,  but 
they  had  less  material  than  we  have  for  judging 
correctly  whether  the  required  conditions  had  been 
fulfilled  in  the  given  case ;  they  liad  a  scantier  ex- 
perience in  detail  of  the  risks  of  error. 

The  abstract  conception  of  the  way  to  use  observed 
agreement  and  difference  in  verifying  a  theory  may 
help  us,  just  as  that  of  the  syllogistic  framework 
may  help  us,  to  see  where  the  weak  point  of  a  given 
piece  of  reasoning  is  to  be  looked  for.  The  specially 
questionable  part  of  a  syllogism  is,  as  we  saw,  its 
middle  term  ;  and  the  specially  questionable  part  of 
any  inductive  process  is  the  assumption  that  named 
circumstances  which  we  have  taken  as  single  may 
safely  be  so  taken.  Just  as  the  claim  that  a  given 
conclusion  rests  on  a  certain  major  and  minor  premiss 
draws  express  attention  to  the  middle  term,  so  the 
claim  that  an  observation  or  experiment  has  been 
conducted  according  to  the  Method  of  Difference 
draws  attention  to  the  implied  assumptions  about 
the  singleness  of  the  circumstances  that  have  varied 
or  persisted.  In  themselves,  and  apart  from  the 
material  knowledge  which  directs  our  use  of  them. 


CH.  nr,§18  REASONING  AND  GENERALISATION  97 

neither  the  inductive  methods  nor  the  Syllogism  have 
any  claim  to  respect.      To  use  them  is  merely  to 
reason  somehow  ;  but  the  correctness  of  our  reasoning 
depends  (where  any  care  is  taken)  on  the  previous 
knowledge  we  can  bring  to  bear  upon  the  facts  we 
handle.     Here,  then,  as  everywhere  throughout  Logic, 
formality  is  the  chief  snare  to  guard  against.     Here 
again  it  is  the  mechanical  nature  of  the  rules  which 
deprives  them  of  value;   the  real  danger  is  not  of 
breaking  or   ignoring   them,  but  of  applying  them 
wrongly.     So  far  as  we  incline  to  dwell  on  the  ab- 
stract form  of  the  inductive  method  or  methods,  for 
instance  by  illustrating  them  in  letters  like  ABC  and 
BC,  ahc  and  he,  or  even  by  choosing  concrete  ex- 
amples where  the  conclusion  is  of  an  indisputable 
kind,  the  result  is  that  we  restrict  attention  to  that 
class  of  inferences  which  least  exemplify  the  need  for 
Logic,  and  the  sources  and  limits  of  its  power  to  deal 
with  difficulty.     There  is  of  course  much  excuse  for 
this.     Every  one  who  has  tried  to  find  examples  of 
inductive  generalisation  must  have  felt  the  force  of 
the  temptation  to  illustrate  rather  the  satisfactory 
than   the    unsatisfactory  use    of  the  methods.       It 
is  not  only  that  satisfactory  conclusions  mean  as  a 
rule  comparative  lack  of  difficulty  in  the  subject- 
matter,  and  that  the  process  is  therefore  more  easily 
followed  and  understood ;  but  an  even  more  enduring 
source  of  the  preference  shown  for  them  is  the  fact 
that   all   faulty  generalisation   involves,  as   such,  a 
departure  from  the  ideal  which  the  method  sets  up, 
and  hence  may  be  said  not  to  illustrate  the  method 
at  all.     Thus  an  instance  of  '  simple  enumeration,' 
It  IS  felt,  can  scarcely  be  considered  an  instance  of 
faulty  use  of  the  Method  of  Agreement,  since  it  does 

7 


08  USE  OF  WORDS  IN  REASONING        i'akti 

not  comply  with  the  requirements  of  the  Canon  ;  and 
the  same  with  the  argument  from  iwst  hoc  to  propter 
hoc  as  illustrating  a  faulty  use  of  the  Method   of 
Difference.      On   the  principles  followed  throughout 
this  book,  however,  and  stated  in  §  35,  a  mere  verbal 
obstacle  like  this  should  have  no  terrors  for  us.     Let 
it  be  consistently  held  that  these  Canons  are  pure 
ideals,  and  all  (concrete  illustrations  of  them  at  once 
become  impossible,  since  there  is  never  any  means 
of  getting  final  satisfaction   that  '  only  one  circum- 
stance' has  varied.      To  say   that  an  ideal  method 
cannot  fail  is  only  to  repeat  in  other  words  that  it  is 
an  ideal ;  and  since  our  actual  inductive  reasonings, 
by  means   of  the   supposed    use    of  these  methods, 
notoriously  can  fail,  it  is  the  interpretations  put  upon 
the  rules,  not  the  rules  in  the  absence  of  all  (-oncrete 
interpretation,  which  are  all  we  can  really  mean  when 
we  speak  of  the  canons  or  axioms  or  methods  as  ad- 
mitting of  illustration. 

And    when    we   judge    them    by    their   use    and 
application,  the  source  at  once  of  their  value  and  of 
their  misleading  power  is  to  be  found  in  uur  previous 
'knowledge.'      In   interpreting  any  o1)served  occur- 
rence   everything     depends    upon    the    views    and 
prejudices  we  already  hold  al)out  the  possilJe  causes 
concerned.     To  this  source  are  to  be  traced  both  our 
success  and  our  failure  in  reaching  truth,  both  our 
acrreements   and   our   differences   of    opinion.      The 
child  who  believes  tliat  the  trees  cause  the  wind,  the 
savage  who  cowers  before  an  eclipse  of  the  sun,  the 
learned  antiquarian  who  thought  the  draught  from 
the  open  window  put  out  the  electric  light,  differs 
not  in  his  mode  of  reasoning  but  in  the  stored-up 
relevant  knowledge  at  his  command,  from  the  wisest 


CH.  rn,§18  REASONING  AND  GENERALISATION  99 

statesman  who  interprets  the  facts  of  history  or  from 
any  specialist,  scientific  or  otherwise,  who  observes 
and  judges  correctly  the  facts  that  belong  to  his  own 
department.  Bare  fact  is  a  thing  unknown  to  us; 
all  facts  are  what  they  are  for  us  by  virtue  of  the 
way  in  which  our  previous  knowledge  helps  or 
hinders  our  understanding  of  the  special  case. 

There  is  perhaps  at  first  sight  an  appearance  of 
something  like  fatalism  about  this  view,  as  if  the 
avoidance  of  error  was  a  matter  wholly  beyond  the 
individual's  control,  and  the  study  of  Logic  therefore 
a  vain  pursuit.  Even  if  it  were  so,  that  would 
scarcely  be  an  argument  against  the  truth  in 
question;  but  tliere  is  no  need  to  expect  from  it 
any  such  consequence.  The  moral  of  the  truth  that 
previous  knowledge  is  reasoning  power  should  not 
be  that  Logic  is  a  worthless  study,  but  only  that  it 
becomes  worthless  in  so  far  as  we  are  content  to  leave 
it  alistract  and  formal.  To  admit  that  Logic  cannot 
make  us  infalli!)le  is  not  to  admit  its  futility,  unless 
indeed  we  persist  in  conceiving  Logic  as  a  system  of 
l)erfect  certainties,— as  the  formal  logician  seeks  to 
conceive  it.  Against  Formal  Logic  the  view  that 
correctness  of  reasoning  depends  on  our  grasp  of  the 
subject-matter  may,  no  doubt,  be  taken  as  hostile, 
but  in  no  way  can  it  be  considered  hostile  to  the 
Logic  which  attempts  to  recognise  everything  that 
helps  to  explain  the  sources  of  success  and  failure  in 
reasoning.  Once  admit,  as  natural  science  now 
admits,  that  there  is  no  finality  of  knowledo-e  of 
the  ways  of  Nature,  and  we  thereby  admit  that 
all  our  inductive  investigations  are  subject  to 
the  same  ultimate  discount.  But  the  distinction 
between   better   and    worse   induction    remains   un- 


H' 


'^     i! 


100 


USE  OF  WORDS  IN  REASOXING        part  i 


affected  by  this  admission,  just  as  the  distinction 
between  motion  and  rest  remains  unaffected  by  the 
consideration  that  absolute  rest  is  unknown.  To 
call  a  statement  true  does  not  nowadays  mean  that 
its  truth  is  of  a  kind  that  can  never  be  improved  or 
corrected,  but  merely  that  it  belongs  to  a  class  of 
statement  which,  judged  by  some  not  wholly  un- 
practical standard,  may  rightly  be  taken  as  satis- 
factory until  the  correction  comes.  Truth,  as  we 
now  conceive  it,  depends  on  the  absence  of  intelligible 
objections  other  than  the  one  vaguest  objection  which 
applies  to  all  known  truths  alike,— the  objection  that 
man  is  fallible.  To  call  a  statement  true  is  therefore 
merely  a  challenge  to  all  the  world  to  find  if  possible 
some  special  fault  with  it,— to  show,  for  instance, 
that  one  of  the  facts  on  which  we  rest  the  statement 
was  in  some  way  wrongly  conceived. 


§  19. — The  Notion  of  a  'Cause' 

The  question  may  be  asked,  how  far  is  it  hera 
intended  to  press  the  quarrel  with  common -sense 
views  of  causation.  It  is  well-known  that  any  one 
who  cares  to  do  so  can  show  that  the  whole  notion 
of  a  Cause  is  riddled  with  verbal  contradictions. 
And  if  we  are  of  those  to  whom  verbal  contradiction 
is  a  hopeless  obstacle  we  shall  decide  that  causation 
is  a  "  mere  practical  makeshift,"  and  discard  all  use 
of  the  notion,— if  we  can.  From  the  point  of  view 
here  taken,  however,  makeshift  truth  is  not  a  thing 
to  be  despised  or  avoided,  but  to  be  used  until  some 
definite  improvement  can  be  made  in  it ;  indeed, 
can  anything  higher  be  said  of  any  truth  than 
that   it   enables   us   to    deal   sufficiently   well   with 


CH.  Ill,  .UO  BEASOXIXG  AND  GENERALISATION  101 

concrete  problems  ?  And  if  there  is  to  be  any  dis- 
tinction at  all  between  better  and  worse  reasoning 
there  must  be  the  distinction  between  better  and 
worse  causal  explanations  of  concrete  events ;  all 
causal  explanations  cannot  l)e  equally  condemned 
as  illusory.  Difficulties  about  Causation,  like  diffi- 
culties about  Truth,  have  no  practical  or  theoretical 
value  when  they  are  pushed  to  the  length  of  destroy- 
ing the  distinction  between  causal  and  other  sequence, 
or  the  distinction  between  truth  and  error.  What 
importance  they  have  depends  upon  their  leading  us 
to  take  care  in  observing,  not  upon  their  tendency 
to  make  us  think  that  knowledge  is  impossible  and 
all  incpiiry  therefore  a  waste  of  time.  If,  however, 
we  keep  in  view  this  necessary  limitation  of  criti- 
cism, a  good  deal  of  advance  may  at  any  rate  be 
made  beyond  inductive  Logic  as  Mill  conceived  it. 
We  may  safely  recognise,  for  instance,  that  in  his 
system  the  abstract  Law  of  Causation  is  given  an 
importance  to  which  it  is  not  entitled,  and  that  the 
assumption  that  things  and  events  consist  of  single 
disjointed  *  circumstances,'  each  of  which  is  '  in- 
variably '  connected  with  some  other,  is  pressed  far 
beyond  the  legitimate  use  and  value  that  can  be 
claimed  for  it.  It  is  an  artificial  view  of  Nature,^ 
and  like  every  artifice  it  must  be  carefully  w^atched 
lest  it  become  misleading. 

First  as  to  the  law  of  Causation.  Those  formal 
logicians  who  include  inductive  Logic  as  part  of  their 
province  ^  seek  for  some  one  comprehensive  principle 

^  To  this  cliarge  it  would  1)6  no  answer  to  say  (what  is  probably  true 
enoiipli)  that  all  writers  on  inductive  Logic  are  aware  of  the  artifice.  The 
question  is  not  whether  they  know,  but  why  they  do  not  use  the  knowledge 
in  constructing  their  system. 

^  We  noticed  al)ove  (p.  9)  that  there  is  some  disagreement  among 
formal  logicians  on  the  question  whether  inductive  Logic  is  properly  to  be 


I*- 


102 


USE  OF  WORDS  IN  EEASOXIXG        part  i 


whicli  may  stand  towards  inductive  conclusions 
generally  in  the  relation  of  major  premiss.  They  fail 
to  recognise  that  any  such  axiom  must  be,  like 
Jevons'  Principle  of  the  Substitution  of  Similars, 
either  a  misleading  half-truth  or  a  meanindess 
truism,  according  as  it  is  made  applicable  or  left 
purely  abstract. 

We  all  agree,  no  doubt,  that  Nature  is  in  some 
sense  uniform ;  only,  when  it  comes  to  interpreting 
this  axiom,  or  to  testing  its  truth,  our  lack  of  omni- 
science becomes  a  serious  obstacle.  The  proportion 
that  our  knowledge  of  Nature  bears  to  the  truths  of 
Nature  cannot,  of  course,  be  known.  But  at  anv 
rate  it  is  small  enough  to  render  surprises  frequent ; 
and  every  such  suri)rise  is  a  case  where  a  sequence 
of  events  (A  followed  by  a)  hitherto  supposed  to  be 
a  case  of  Nature's  Uniformity — a  case  of  *  invariable  ^ 
sequence' — turns  out  to  be  more  complex  than  we 
imagined,  and  the  occurrence  of  a  is  found  to  be, 
partly  at  least,  conditioned  by  other  things  than  A. 
What  looks  to  us  the  same  cause  is  often  found  not 
to  produce  the  same  effect;  what  looks  to  us  the 
same  effect  is  often  found  to  have  been  produced  by 
different  causes.  That  which  is  true  of  a  thinfr  is 
often  untrue  of  another  thing  which  seems  its  '  like, 
equal,  or  equivalent.'  And  until  our  knowledge  of 
Nature  is  complete  we  shall  never  be  free  from  these 
surprises,  for  the  progress  of  knowledge  necessarily 
involves  the  correction  of  rules  which  we  have 
hitherto   regarded  as  trustworthy.      And  the   more 

considered  part  of  their  subject  or  not ;  but  they  would  probably  agree  that 
any  Lof^c  must  be  either  formal  or  else  not  'scicntihc' 

'  Though  Mill  sometimes  preferred  the  expression  '  invariable  and  un- 
eonditumal'  at  other  times  ((.7.  vol.  i.  p.  393)  he  siiw  that  "the  antecedent 
which  is  only  conditionally  invariable  is  not  the  invariable  antece<lent,"  and 
that  therefore  the  word  '  invariable '  is  suHicient  by  itself. 


CH.  Ill,  §19  REASONING  AND  GENERALISATION  103 

comprehensive  the  rule  the  more  this  applies ;  the 
small  generalisations  which  guide  us  in  a  strictly 
limited  branch  of  inquiry  take  a  less  extended  risk 
than  those  which  pretend  to  cover  the  whole  field  of 
human  knowledge. 

Even  if  we  break  up  our  Law  of  Causation  into  a 
group  of  inductive  canons,  we  are  still  framing  highly 
comprehensive  rules,  and  the  danger  is  that  because 
they  are  undeniable  wdien  made  abstract  we  shall 
overlook  their  shortcomings  when  they  are  made 
applicable.  If  there  is  a  sense  in  which  they  are  true, 
it  is  a  sense  which  ever  eludes  our  grasp,  for  as  soon 
as  we  tie  them  down  to  concrete  applications  they 
cease  to  be  true  in  the  whole  extent  of  their  generality, 
and  so  become  misleading  wdien  used  as  major  pre- 
misses. For  the  purpose  of  drawing  any  particular  \ 
conclusion  the  vague  belief  that  Nature  is  somehow 
uniform  is  irrelevant ;  the  only  relevant  question  is 
whether  we  have  conceived  some  particular  piece 
of  supposed  uniformity  without  important  error.  It 
does  not  help  us  to  know  that  a  given  event  must 
have  had  some  cause,  and  will  have  some  effect ; 
always  the  question  is  precisely  what  is  essential  and  \ 
what  is  accidental  to  this  or  that  fact  observed. 

Secondly,  as  to  the  disjointed  view  of  the  facts 
or  circumstances.  It  is  admitted,  of  course,  that  all 
explanation  of  events — and  indeed  the  very  form  of 
the  question,  *  what  is  essential  to  what,'  or  *  what 
leads  to  wdiat' — involves  the  conception  of  separ- 
able portions  of  an  occurrence,  however  strictly  con- 
tinuous the  stream  of  occurrence  may  be.  But  there 
is  a  great  difference  between  admitting  the  practical 
need  of  this  assumption  and  forgetting  its  artificiality. 
Granting  that  in  no  way  can  we  hope  to  reach  a 


104  USE  OF  WORDS  IN  REASONING        parti 

complete  understanding  of  the  ultimate  nature  of 
causation,  still  to  suppose  the  course  of  Nature  really 
continuous  and  only  artificially  discontinuous  enables 
us  at  least  to  remember  that  between  any  two  stages 
there  is  room  for  intermediate  ones,  or  that  if  A  and  a 
are  separated  at  all  the  filling  of  the  gap  between  them 
is  (along  with  A)  part  of  the  cause  of  a,— part  of  what 
leads  to  a.  Immediacy  of  sequence  would,  no  doubt, 
be  convincing  evidence  of  causation  ;  only  it  is  well 
to  remember  that  a  really  immediate  sequence  is 
never  found,— that  to  separate  A  and  a  is  always  to 
leave  out  of  sight  the  l)ridge  which  as  a  matter  of 
fact  connects  them.  Mill  was  content  (p.  541)  to 
note  this  case  as  occasional. 

Similarly  with  the  separation  of  A  from  the  con- 
temporary circumstances  BCD  .  .  .  Z.  To  admit  the 
artificiality  of  this  separation  is  to  admit  a  corre- 
sponding vagueness  in  our  assertion  that  the  sequence 
A  followed  by  a  is  *  unconditional,'  and  therefore 
quite  strictly  invariable.  Every  experienced  case  of 
A  differs  somehow  from  every  other,  and  the  question 
which  of  its  many  details  are  essential  to  its  A-ness, 
and  which  are  accidental  to  that  and  yet  are  con- 
ditions of  the  effect  a,  is  the  question  of  questions  in 
deciding  how  to  specify  a's  cause.  So  far  as  we  have 
to  be  content  with  an  unsatisfactory  answer  to  it, 
*  unconditionality '  as  evidence  of  causation  is  a 
broken  reed. 

Of  course  we  do  not  remove  the  mystery  of  causa- 
tion,^ of  growth,  or  of  change,  by  *  beating  it  out 
thin/  The  problem  how  anything  can  become  some- 
thing else  is  just  as  difficult,  theoretically,  when  the 
change  occurs  in  the  millionth  part  of  a  second  as 
when  it  takes  a  million  years.     All  that  we  can  do 


« 


u 


CH.  Ill,  §19  REASONING  AND  GENERALISATION  105 

by  making  the  interval  short  is  to  make  a  more 
direct  appeal  to  our  existing  knowledge  of  what  leads 
to  what.  To  see  how  one  thing  leads  to  another  is 
never  quite  to  get  a  vision  of  continuity,  but  only 
to  recognise  as  familiar  the  separate  links  that  make 
up  the  chain  ;  and  our  familiarity  with  any  one  of 
the  links,  though  it  may  conduce  to  carelessness  of 
inquiry,  is  no  complete  guarantee  that  we  know  all 
that  is  worth  knowing  about  it. 

From  all  this  it  appears  that  the  distinction  be- 
tween a  causal  law  and  a  merely  empirical  law  cannot 
l>e  made  quite  satisfactory.  That  generalisations  are 
better  in  so  far  as  we  can  see  causation  behind  them 
is  a  statement  which  has  some  convenience,  but 
only  when  we  do  not  ask  too  closely  what  it  means. 
For  then  we  are  led  either  to  deny  or  to  admit  our 
ignorance  of  the  precise  nature  of  causation.  In  the 
former  case  the  reality  of  that  inevitable  ignorance  is 
sure  to  lead  us  into  false  positions  thinly  disguised 
by  evasive  language.  In  the  latter  case  we  admit 
indirectly  that  so-called  cases  of  causation  are  nothing 
but  those  generalisations  which  we  think  most  nearly 
proved,  and  that  therefore  to  say  that  a  general  rule 
is  proved  when  it  is  found  to  be  causal  only  means 
that  it  is  proved  so  far  as  its  proof  is  forthcoming. 

Our  ignorance  of  the  meaning  of  causation  is  of 
course  only  the  same  kind  of  ignorance  as  that  of 
the  meaning  of  *  Truth.'  The  abstract  idea  of  causa- 
tion, like  that  of  Truth,  is  among  the  most  familiar 
of  our  mental  possessions.  Indeed,  we  can  form 
no  conception  of  what  a  mind  would  be  like  which 
attempts  to  think  without  making  some  distinction 
between  truth  and  falsity,  and  some  distinction  be- 
tween connections  which   are  essential  (causal)  and 


106 


USE  OF  WORDS  IN  REASONING        part  i 


those  which  are  accidental.  What  in  both  cases 
we  do  not  know  is  how  to  get  sufficient  security 
in  applying  these  distinctions.  Practically  what  we 
do  is  to  use  varying  standards  of  accuracy,  and 
to  be  content  when  we  get  near  enough  for  some 
purpose  we  have  in  view.  And  as  regards  the 
question  what  caused  Y  (or  whether  X  did  or  did 
not  cause  Y)  on  a  given  occasion,  our  view  is  deter- 
mined partly  by  the  other  views  of  causation  we  have 
already  acquired  and  partly  by  wliat  may  be  called 
the  apparerd  unconditionality  of  the  sequence.  Every 
observation  or  experiment  is  a  view  of  an  '  event,' — 
a  change ;  and  the  conception  of  a  change  involves 
not  only  that  of  a  rehitively  unchanging  background 
against  which  the  change  stands  out  to  be  seen,  but 
also  that  of  an  event  divisible  (ideally)  into  two 
portions,  which  we  call  the  antecedent  and  the  conse- 
quent events.  Whenever  an  occurrence  of  any  sort 
is  observed,  there  is  no  room  for  doul)t  that  some- 
thing has  caused  something;  and  the  sole  doubt 
attaches  to  the  question  what  precisely  caused  what. 
To  the  intricacies  of  such  a  question  no  perfectly 
final  end  is  to  be  expected,  though  a  working  satis- 
ftiction  may  often  be  got  with  a  little  trouble,  and  a 
delusive  one  still  more  easily. 

And  the  nearer  we  get  to  a  satisfactory  account  of 
what  caused  what  in  a  given  occurrence  the  more  the 
doubt  that  remains  tends  to  become  a  doubt  whether 
the  names  by  which  we  describe  the  cause  and  the 
effect  respectively  are  sufficiently  accurate.  In  the 
grosser  kinds  of  error  of  explanation, — for  instance 
where  in  observing  a  conjuring  trick  we  fail  to 
notice  the  hidden  cause  and  set  down  the  result  to 
something  which  had  no  share  in  it, — there  is  what 


cir.  m,§19  REASONING  AND  GENERALISATION  107 

every  one  would  naturally  call  a  downright  mistake, 
rather  than  an  insufficient  or  misleading  description. 
But  it  is  evident  that,  since  fineness  of  error  consists 
in  the  mingling  of  truth  with  error,  errors  of  explana- 
tion are  fine — and  therefore  difficult  to  deal  with,  and 
therefore  of  special  importance  to  Logic — in  propor- 
tion a^  the  *  X '  which  we  take  to  be  cause  is  really 
2^art  of  the  cause  ;  so  that  the  error  consists  in  descril)- 
ing  the  cause  as  X,  rather  than  as  X-hZ.  For  if 
)»oth  X  and  Z  are  necessary  to  the  production  of  Y, 
then  the  generalisation  that  X  and  Y  are  essentially 
connected  facts  is  a  mere  half-truth ;  it  holds  good 
only  of  those  cases  of  X  which  are  also  cases  of  Z, 
and  will  mislead  us  if  we  apply  it  more  widely. 

In  spite  of  the  fact,  then,  that  inductive  logicians 
generally  dwell  at  some  length,  and  often  most  in- 
structively, on  the  practical  danger  attaching  to  our 
judgments  about  the  behaviour  of  '  only  one  circum- 
stance,' there  may  nevertheless  be  room  for  a  still 
further  extension  of  the  movement  of  which  Mill 
was  one  of  the  pioneers.  What  we  need  is  to  have  the 
recognition  of  this  danger  incorporated  into  logical 
theory,  and  not  merely  joined  on  to  it  by  an  after- 
thought. Mill  himself,  as  we  have  seen  (p.  95), 
sometimes  forgot,  in  speaking  of  the  Method  of  Differ- 
ence,  that  in  every  careful  but  false  induction  the 
observer  imagines  that  he  has  used  this  method  as^ 
nearly  as  possible;  forgot,  therefore,  that  however  rigor- 
ously certain  the  abstract  Method  of  Difference  may  be, 
the  only  Method  of  Difference  that  we  can  apply  gives 
us  a  false  security.  Formal  inductive  logicians  of  the 
present  day  take  a  rather  half-hearted  course  between 
excessive  belief  in  the  value  of  the  methods  and  due 
recognition  of  their  defects  as  a  part  of  logical  theory. 


WB 


108 


USE  OF  WORDS  IN  REASONING        part  i 


For  instance,  Mr.  Carvetli  Read  ^  expresses  a  wide- 
spread opinion  when,  after  speaking  of  the  danger, 
he  says : — 

It  is  right  to  touch  uix)n  this  well-known  sceptical  topic ;  but 
to  insist  much  upon  it  is  not  a  sign  of  good  sense.  The  works 
of  Ilerschel,  Whewell,  and  Jevons  should  be  consulted  for  the 
various  methods  of  correcting  observations,  by  repeating  them, 
averaging  them,  verifying  one  experimental  process  by  another 
always  refining  tlie  methods  of  exact  measurement,  multiplying 
the  opportunities  of  error  (that  if  any  exist  it  may  at  last  show 
itself),  and  by  other  devices  of  what  may  be  calle<l  Material 
Logic.  But,  probably,  only  many  years  spent  in  the  study  and 
personal  manipulation  of  scientific  processes,  can  give  a  just 
sense  of  their  etlectiveness  ;  and  to  st^md  by,  suggesting  academic 
dou))ts,  is  easier  and  more  amusing. 

With  most  of  this  we  can  all  agree,  and  its  chief 
defect  is  the  encouragement  it  seems  to  give  to  the 
popular  belief  that  the  suggestion  of  academic  doubts 
is  never  made  except  in  the  interests  of  idle  amuse- 
ment. That  there  are  all  sorts  of  sceptics  I  would 
not  deny,  but  why  should  we  consider  only  the 
variety  of  them  who  suggest  their  doubts  in  this 
spirit  ?  Why,  especially,  should  we  view  their  exist- 
ence as  any  reason  for  concealing  the  real  weakness 
of  the  abstract  inductive  methods?  A  scientific 
investigator,  for  example,  acquires  his  scepticism  not 
at  the  cost  of  his  good  sense  and  practical  capacity 
but  rather  by  the  exercise  of  them.  Mr.  Read's  vague 
phrase  '*  to  insist  much  on  it "  seems  also  to  point  to 
some  misapprehension  of  the  best  way  to  combine 
scepticism  with  good  sense  and  practical  ability; 
which  is  not  by  applying  a  limited  and  fixed  amount 
of  scepticism,  but  by  intelligently  selecting  the  right 
occasions  for  applying  respectively  as  much  and  as 
little  as  possible. 

*  Logie^  Deductive  and  Inductive^  p.  194. 


CH.iir,.^19  REASONING  AND  GENERALISATION  109 

It  may  be  noticed  also  that  the  task  of  improving 
the  theory  of  Logic,  and  that  of  applying  it  to  actual 
arguments,  are  to  this  extent  different :  that  while 
the  degree  of  care  and  refinement  required  for  the 
latter  task  is  determined  entirely  by  the  degree  of 
correctness  which  will  serve  the  practical  purpose 
contemplated,  no  limit  can  be  set  to  the  care  and 
refinement  needed  for  the  former, — except,  of  course, 
the  limit  noticed  above  at  p.  101.  Apart  from  this, 
the  only  limit  is  a  shifting  and  personal  one,  set  by 
the  power  of  the  logician  to  see  and  express  intelli- 
gibly diflicult  and  complicated  truths.  The  extent  of 
this  power  is  dependent,  among  other  things,  on  the 
extent  to  which  the  science  and  civilisation  of  the 
day  have  developed  the  resources  of  language.  And 
since  the  effectiveness  of  any  general  device  for 
testing  inductive  inquiries  is  never  perfect,  and  is  not 
equally  strong  on  all  occasions  of  its  use,  you  achieve 
more  by  studying  its  imperfections  and  relating  them 
to  this  or  that  kind  of  occasion,  than  by  shutting  off 
your  critical  power,  vaguely  conceiving  of  the  method 
as  perfect  or  nearly  so,  and  adding  occasional  after- 
thoughts under  haphazard  compulsion  from  stubborn 
facts  that  refuse  to  be  silenced.  Even  though  the 
theory  of  Logic  must  lag  a  little  behind  its  applica- 
tion by  those  engaged  in  special  scientific  work,  there 
seems  to  be  no  reason  why  the  logician,  as  such, 
should  attempt  to  hold  it  back.  As  we  shall  see  in 
chapters  vii.  and  viii.,  the  childish  or  playful  sceptic 
is  harmless  in  every  w^ay,  and  easily  disposed  of. 
We  need  not  make  a  bugbear  of  him,  and  least  of  all 
in  the  name  of  Logic  or  Philosophy.^ 

^  On   this    }>oint  see  also  my  book  on  Distinction^  pp.  223,  224  ;  and 
Mind,  1895,  pp.  303-306. 


CHAPTER    IV 


IlEASOXIXCJ    AND    JUDGMENT 


8  20. — A  Problem  of  Definition 

We  next  come  to  certain  difficulties  about  the 
definition  of  *  reasoning,'  and  to  the  consequences  of 
admitting  them  to  be  insurmountable.  The  puzzle  is 
to  distinguish  clearly  between  reasoning  and  certain 
otlier  mental  processes,  or  at  least  mental  processes 
which  are  commonly  called  by  other  names.  It  is 
difficult,  I  mean,  to  distinguish  them  in  concrete 
cases, — for  of  course  it  is  always  easy  enouf^h  to 
mention  a  pair  of  contrasted  words.  We  can  mark 
off  'reasoning,'  in  the  abstract,  from  'simple  un- 
reasoned judgment,'  but  can  we  apply  the  distinction 
correctly  ?  In  §  24  we  shall  notice  the  kind  of 
importance  this  question  has  for  Logic  as  contrasted 
with  Psychology. 

'  Reasoning '  is  one  of  the  many  words  which  do 
not  require  translation.  No  one  who  asks  for  an 
explanation  of  it  is  quite  in  the  position  of  those  who 
first  make  acquaintance  with  a  purely  technical  term. 
We  all  know  something  about  its  meaning,  since  the 
word  is  freely  used  in  everyday  language.  However 
vaguely  we  may  conceive  the  nature  of  the  mental 
act  so  described,  we  think  of  it  as  contrasted  with 


CH.  IV,  .^  20    REASONIXG  AND  JUDGMENT 


111 


simpler  acts  of  mind, — in  the  same  sort  of  way  as  a 
chain  may  be  contrasted  w^ith  any  one  of  its  single 
links.  And  this  conception  of  it,  w^e  find,  is  expressly 
put  forward  and  dwelt  upon  in  the  traditional  Logic. 
Reasoning,  or  Liference,  is  something  more  than  mere 
Judgment,  we  are  told^ ;  the  latter  is  not  reasoning 
l>ecause  it  is  not  the  movement  from  facts  (or  pre- 
misses) to  a  conclusion.  But  there  the  old  locficians 
leave  the  difficulty,  w^ithout  apparently  being  aw^are 
that  any  difficulty  exists.  It  is  the  vice  of  the 
abstract  or  formal  treatment  of  Logic  everywhere 
that  it  leaves  untouched  the  points  that  are  most 
interesting  and  instructive.  If  we  make  the  verbal 
distinction  between  reasoning  and  judgment  turn  on 
the  supposition  that  the  latter  is  absolutely  unre- 
flective,  innocent  of  grounds  or  reasons,  does  not 
proceed  from  data  to  conclusion,  or  is,  in  a  word,  a 
single  link  and  not  itself  a  piece  of  chain,  then  it 
becomes  a  highly  pertinent  question  whether  any 
such  mental  acts  are  in  fact  to  be  discovered,  and  if 
so  which  exactly  they  are.  However  sharply  X  in 
the  abstract  is  distinguished  from  Y,  any  concrete 
instance  of  either  may  be  challenged  to  show  its  right 
to  the  name,  and  until  the  challenge  is  satisfactorily 
answered  it  remains  only  a  case  of  so-called  X  or  so- 
called  Y.  When  an  instance  is  taken  we  may 
perhaps  by  looking  carefully  at  it  be  able  to  see  that 

^  In  modern  textbooks  tlie  distinction  is  scarcely  made  so  prominent  as 
formerly.  Whately  is  perhaps  the  most  recent  instance  of  a  writer  who  can 
he  said  to  take  the  old  division  between  **  the  three  oj>erations  of  Thought  " 
(simple  apprehension,  judgment,  and  reasoning)  as  rigidly  as  possible.  See 
his  chai>.  i.  §  1.  And  in  his  Essay  on  the  province  of  reasoning  he  goes  so 
far  as  to  say  that  the  process  of  observation  and  experiment  is  not  a  process 
of  argument  ;  and  again,  that  "  the  bare  jnocess  of  reasoning,  i.e.  deducing 
a  conclusion  from  i)remisses,  must  ever  remain  a  distinct  operation  from  the 
assumption  of  premisses."  For  an  interesting  statement  of  the  problem 
from  a  modern  point  of  view,  see  Bosanquet's  Logic,  vol.  ii.  chap.  i. 


112 


USE  OF  WORDS  IX  EEASOXIXG        pakt  i 


it  is  not  really  so  simple  as  it  seems  ;  we  may  see  that 
*  so-called  Y'  shares  in  the  nature  of  X  to  some 
extent,  and  so  cannot  be  sharply  contrasted  with  it. 
Now  we  may  either  raise  this  question  or  not,  but  we 
had  better  make  up  our  minds  which  course  we  will 
take.  At  least,  we  must  not  set  out  to  inquire  into 
the  difference  between  reasoning  and  instinctive 
judgment,  and  then  be  satisfied  to  solve  it  by  mere 
definition.  And  it  is  not  always  easy  to  remain 
aware  of  this  risk,  especially  when  it  is  concealed  by 
the  use  of  technical  lanf]^uaore.     As  soon  as  we  besrin 

kD  CD  o 

to  talk  of  *  reasoning  strictly  so-called,'  or  *  reason- 
ing in  the  proper  sense  of  the  term,'  we  are  professing 
a  kind  of  knowledge  which  is  far  less  within  our  reach 
than  a  ready  use  of  these  phrases  may  allow  us  to 
suppose. 

§  21. — Some  False  Solutions  of  the  Problem 

There  are  two  chief  fields  in  which  the  difference 

between  reasoning  and  instinct  may  be  sought  for, 

in  comparison  between  the  deliberate  and  the  rapid 
judgments  of  man,  or  again  between  the  judgments 
of  man  and  those  of  the  lower  animals  ;  and  in  both 
the  danger  of  a  sham  settlement  of  the  question 
should  be  kept  in  view.  The  difficulty  is  that  in 
both  cases  the  inquiry,  if  pressed  far,  reaches  a  point 
at  which  the  verifiability  of  our  theories  vanishes. 
When  a  man  discovers  in  five  minutes  the  cause  of 
the  stoppage  of  a  clock  we  all  agree  that  he  reasons 

it  out ;    but   we  do  not  all   agree  how  to  name 

whether  as  reason  or  as  instinct — processes  of  thouf^ht 
which  are  performed  much  more  rapidly  ;  for  instance, 
the  general's  sudden  decisions  in  a  battle,  or  the 
orator's  choice  of  words  and  tones  and  gestures.     Is 


ciL  IV,  g  21     EEASOXIXG  AXD  JUDGMEXT  113 

not  our  uncertainty  whether  to  call  such  judgments 
reasoned  or  intuitive  due  to  the  fact  that,  in  pro- 
portion to  the  rapidity  of  the  judgment  and  the  mass 
of  details  judged,  the  difficulty  increases  of  knowing 
what  really  took  place  in  the  mind  concerned  ?  Even 
if  the  mind  in  question  is  our  own,  we  can  find 
innumerable  cases  of  rapid  judgment  where  memory 
can  tell  us  nothing  of  the  steps  ;  we  are  left  wonder- 
ing how  we  suddenly  came  into  our  vision  of  the 
truth,  or  why  we  acted  so  rightly  on  the  spur  of  the 
moment.  Because  we  cannot  in  these  cases  follow 
the  action  of  the  mind,  we  do  not  know  whether  it 
does  or  does  not  resemble  reasoning  in  every  respect 
except  the  time  it  occupies.  For  all  we  know,  the 
apparent  simplicity  of  the  process  may  be  an  illusion, 
like  the  apparent  simplicity  of  a  flash  of  lightning. 
As  our  eyesight  fails  to  report  the  to-and-fro  move- 
ments of  the  lightning,  so  our  retrospection  of  a 
rapid  judgment  may  fail  to  report  the  steps  by  which 
our  indecision  gave  place  to  decision  when  our  ap- 
parently instantaneous  judgment  was  reasoned  out. 

In  the  comparison  of  our  judgments  with  those  of 
the  lower  animals  the  chief  difficulty  is  that  of  inter- 
preting correctly  the  signs,  or  of  clearly  imagining  what 
goes  on  in  a  mind  which  is  to  an  unknown  extent  both 
like  and  unlike  our  own.  Ignorant  as  we  are  of  the 
precise  nature  of  the  differences  among  human 
mmds,— e.g'.  between  those  of  men  and  women,  or 
black  and  white,  or  prince  and  pauper,  or  Protestant 
and  Catholic,  or  English  and  Continental  —  we  are 
naturally  much  more  so  when  the  minds  compared 
are  those  of  the  man  and  the  dog.  Professor  William 
James  ^  supplies  an  interesting  set  of  animal  stories 

*  Principles  of  Psychology ^  ii.  348. 

8 


114 


USE  OF  WORDS  IN  REASONING         part  i 


collected  from  various  sources,  and  seems  to  incline 
to  the  view  that  none  of  them  are  cases  of  reasoning. 
But  the  difficulty  is  to  find  any  distinct  ground  of 
difference,  any  characters  which  differ  otherwise  than 
gradually  from  the  clearest  cases  of  reasoning.     Of 
course  we  can  make  verbal  i^rounds  of  difference,  in 
any  numl)er  we  please  ;  but  that  would  be  to  attempt 
to   solve   the   problem  by  mere   detiniiion;  it  would 
only  alter  the  form  of  the  difficulty.     We  might,  for 
example,    contend   that   *'  simple  contiguous  calling 
up   of  one   whole   by   another   is   quite  sufficient   to 
explain   the  phenomena."      But  then    we  only  raise 
the    question    whether  wliat   is  called  the   **  simple 
contiguous "  process  differs  essentially   from   reason- 
ing,— a  point  about  which  there  may  notoriously  be 
two  opinions,  and  a  (juestion  which  is  itself  in  danger 
of  being  stilled  by  mere  detinition.     Similarly  there 
is  no  real  help  to  be  got  from  making  the  distinction 
turn  on   the  question  whether  the  circumstances  in 
which  the  act  takes  place  are  strange  or  familiar.      If 
any  of   our  experiences  were   absolutely   strange   or 
novel  we  could  not  reason  from  them  at  all,  and  if  any 
were  entirely  familiar  our  conclusion  would  not  have 
advanced  beyond  our  data.     But  since,  as  a  matter 
of  fact,  all  our  experiences  contain  a  mixture  of  more 
and  less  familiar  elements,  this  account  of  the  turning- 
point  of  the  distinction  is  again  no  more  than  verbal. 
It  merely  alters  the  fonn  of  the  difficulty,  by  raising 
the  question    how  to    distinguish    Ijetween    circum- 
stances which  as  a  whole  deserve  to  be  called  stransre 
and   those    which    as  a   whole  deserve  to  be  called 
familiar.     Since  the  difficulty  is  a  real  one  it  survives 
all  changes  in  its  external  form. 


CH.iv,5^22     REASONING  AND  JUDGMENT 


115 


:J 


§  22.— Judgment  as  Process  and  as  Instrument 

Let  us  turn  now  to  another  suggestion.     Can  we 
make  a  clear  distinction  between  judging,  as  the  for- 
mation of  judgments,  and  reasoning  as  the  employment 
of  judgments  already  formed  ?     That  the  distinction 
has   some    value    may   be   seen    from  the  difficulty, 
noticed  in  S$J  4  and  G,  of  classing  our  most  undeniable 
axioms  as  judgments  at  all,  since  they  involve  no  act 
of  rejection.     There  is   no  intelligible  formation   of 
judgment  in  the  case  of  our  most  fundamental  axioms, 
since  we  cannot  in  imagination  put  ourselves  back 
to  the  time — if  there  ever  was  a  time — when  a  choice 
was  allowed  us   between  believing  and  disbelieving 
them,  and  when  we  answered  *  yes '  where  we  micrht 
conceivably    have    answered    *  no/      On    the    other 
hand    it    looks    as   if  we  could    and    did    use   these 
axioms,  and  as    if  the  use  of  them  in  connection 
With  minor  premisses  was  precisely  what  is  meant  by 
reasoning.     Passing  by  the  question  (discussed  above, 
p.   33)   what  is  the  real  nature  of   the  widest  and 
most  abstract  major  premisses  we  can  actually  use, 
we  may  still  admit  that  there  is  a  difference  between 
forming  and  using  a  judgment ;  the  difficulty  is  to 
disentangle    the   two    operations   as  we    find    them 
combined  in  any  judgment  we  can  examine.      The 
formation  of  a  judgment  is  often  a  long  process,  in- 
'•luding  many  checks  and  fresh  starts  ;  and  it  is  often 
extremely  difficult  or  impossible  to  say,  except  quite 
arbitrarily,  when  it  comes  to  an  end.     For  those,  of 
course,  who   possess  an  infallible  guide,   it  ends    as 
soon  as  the  oracle  has  spoken,  but  for  the  rest  of  us 
even   the   most   authoritative    pronouncement    may 


116 


USE  OF  WORDS  IN  REASONING        part  i 


need  revision  at  any  time.  And  these  checks  and 
tentative  movements  that  occur  while  tlie  jud^^ment 
is  in  the  making  consist  in  treating  the  half-formed 
judgment  as  a  hypothesis,  and  usiny  it  to  deduce 
imaginary  consequences.  Then  if  reasoning  is  de- 
fined as  the  using  of  judgments  it  cannot  l)e  contrasted 
(except  verbally,  or  in  the  abstract)  with  the  forma- 
tion of  judgments,  since  it  is  a  part  of  that  operation 
wherever  they  are  formed  with  any  care.  Moreover, 
it  is  at  best  an  unverified  assumption  to  suppose 
that  even  in  our  hastiest  and  least  considered  judg- 
ments reficction  phiys  no  part.  Of  course  nothing 
is  commoner  than  to  talk  of  people  making  '  wdiolly 
unreasoned'  assertions,  or  *  jumping  to  conclusions,' 
or* speaking  without  reflection.'  But  unless  these 
are  merely  forcil)le  ways  of  saying  that  the  person 
so  proceeding  has  not  used  reflection  enough,  it  is 
hard  to  see  how  they  can  be  justified.  At  any  rate 
the  only  ground  we  have  for  denying  the  presence  of 
reflection  in  judgments  where  we  cannot  directly  per- 
ceive it  is  the  same  kind  of  ground  that  w^e  formerly 
had  for  denying  the  oscillations  of  the  lijrhtninfr  or 
any  of  the  unsuspected  facts  which  instantaneous 
photography  has  brought  to  our  notice. 

Although,  therefore,  we  cannot  quite  clearly  dis- 
tinguish between  the  formation  of  judgments  and 
the  use  of  them  when  formed,  and  cannot  imagine 
the  formation  of  a  judgment  as  a  process  with  a 
clearly-marked  beginning  or  end,  we  may  perhaps 
conceive  of  reasoning  as  the  reflective  movement  of 
thought  which  accompanies  the  formation  of  a 
reasoned  judgment  at  all  its  stages,  rather  than  as  the 
forward-reaching  movement  which  it  is  the  special 
business  of  reflection  to  control  and  guide  to  safety. 


CH.  IV,  .^  23     REASONING  AND  JUDGMENT  117 

That  the  influence  of  reflection  is  always  beneficial 
there  is  no  need  to  assume, — sometimes  first  thoughts 
are  best;  but  at  any  rate  criticism  involves  and 
begins  with  reflection,  and  reasoning  depends  for  its 
value  upon  a  judicious  admixture  of  criticism.  And 
the  w^ork  of  reflection  consists  chiefly  in  pruning 
away  exul)erances  of  belief  and  in  keeping  an  eye 
upon  the  likelihood  of  error.  In  the  more  leisurely 
kinds  of  reasoning,  where  the  process  can  be  observed, 
we  find  the  usual  result  of  reflection  to  be  that  some 
parts  of  the  judgment  grow  safer  against  attack  and 
fuller  of  meaning,  while  other  parts  wither  away  or 
lose  importance.  Hypothesis  and  verification,  each 
I)erformed  under  a  sense  of  the  need  for  analysing 
'  facts '  till  their  essence  is  discovered,  constitute 
the  framework  of  its  method. 


§  23. — Reasoning  as  the  Advance  to  a 

Conclusion 

A  further  ground  for  doubting  whether  a  sharp 
distinction  can  ever  l)e  made  between  reasoning  and 
judgment  is  that  when  we  take  the  word  reasoning 
in  the  second  of  the  tw^o  senses  noted  at  p.  58, — when 
we  do  not  view  reasoning  as  reflection  but  merely  as 
the  forw^ard  movement  from  data  to  '  new  conclusion,' 
—we  inevitably  get  drawn  into  the  difficulty  of  dis- 
tinguishing between  one  judgment  and  '  another,' 
or  between  one  judgment  and  a  number  of  judgments. 
These  difliculties  do  not  exist  for  the  formal  logician, 
—or  only  so  far  as  he  nov/  and  then  deserts  his 
principle  that  sentence  and  assertion  are  the  same, 
— since  sentences  are  distinguishable  from  each  other, 
and  are  therefore  as  easily  counted  as  a  row  of  figures. 


1 


118 


USE  OF  WORDS  IN  REASONINa        part  i 


But  it  is  far  from  being  jiii  easy  (juestion  liow  mucli 
change  in  a  given  judgment  we  ought  to  regard  as 
constituting  *  otherness/ — especially  if  we  admit  tliat 
the  formation  of  a  judgment  is  rather  a  case  of  growth 
than  of  sudden  perfect  achievement.  May  not  the 
so-called  leap  to  new  conclusions  he  also  just  as  truly 
a  case  of  growth  (  Tossihly  any  stages  or  halting- 
places  we  find  it  convenient  to  recognise  are  only 
artificially  marked  otf  from  each  other  l>v  dropjnng 
out  of  sight  the  links  that  come  hetwccn.  If  any 
steps  at  all  are  to  he  recognised — any  passage  /rowt 
something  to  something  else — what  is  to  decide  the 
length  of  these  steps;  what  is  to  prevent  our  search- 
ing between  any  so-called  steps  till  we  find  a  bridge 
over  the  gap  between  them  and  see  the  end  only  as 
the  development  of  the  beginning,  rather  than  as 
something  distinct  from  it.  If  so,  then  the  dillerence 
between  a  piece  of  reasoning  and  a  simple  judgment 
would  be  merely  that  the  former  (when  made  explicit) 
is  an  artificial  isolation  of  two  stages  of  the  hitter's 
growth.  And  that  would  help  to  explain  our  notori- 
ously common  failure  to  *  give  our  reasons'  for  a 
conclusion.  By  the  time  a  halting-place  (a  concdusion) 
is  reached  we  have  kicked  away  many  of  the  ladders 
by  which  we  reached  it,  and  our  remembrance  of  the 
details  of  the  climb  has  suffen^d  some  loss :  a  vacrue 
and  general  account  of  the  steps  is  usually  all  that 
can  be  given,  and  this  makes  them  seem  more  dis- 
connected than  they  were. 

§  24. — The  Effect  of  Admitting  the  Difficulty 

The  problem   what  to  do  with  these  diiliculties, 
once  we  have  allowed  ourselves  to  see  them,  presses 


CH.iv,§24     REASONING  AND  JUDGMENT  119 

for  answer  ;  and  our  choice  seems  to  lie  between  some 
kind  of  *  my thology  ' — i.e.  explanatory  hypothesis — 
and  some  kind  of  non-explanatory  verl)iage.  If  we 
dectide  against  the  latter  course,  and  confess  our 
uncertainty  as  to  the  inmost  nature  of  rapid  intuition, 
we  have  nothing  for  it  but  to  resort  to  openly  specu- 
lative methods.  We  must  guess,  and  then  see  what 
results  from  our  guesses,  what  help  they  give  or  what 
i-ontradictions  they  lead  to. 

Let  us  make  the  hypothesis,  then,  that  all  judg- 
ment, even  the  least  apparently  rational,  would  be 
seen  to  be  precisely  the  same  in  structure  as  reasoning 
or  infereiK-e  if  we  could  magnify  it  sufficiently,  and 
<-()uM  fix  the  moving  picture  sutticiently,  to  render 
vision  of  it  possible ;  that  in  the  briefest  flash  of 
intelligence  there  is  the  same  comparison  of  provisional 
theories  with  apparent  facts  as  in  the  most  deliberate 
reasoning,  only  ipiicker  and  vaguer  and  less  in 
<|uantity  ;  and  that  there  is  always  room  for  more  of 
this  '  reflection '  except  so  far  as  practical  needs, 
external  or  internal,  put  an  end  to  the  process  and 
allow  us  to  claim  to  have  reached  a  conclusion ;  and 
that  therefore  the  end  of  a  piece  of  reasoning  is 
related  to  its  beginning  in  just  the  same  way  that  a 
more  formed  judgment  is  related  to  a  less  formed  one, 
the  relation  in  both  cases  bein^j  one  of  ofrowth  as 
ijciween  l)ud  and  flower  or  child  and  man,  and  the 
line  drawn  between  datum  and  conclusion  being  just 
«i^  arbitrary  as  those  we  draw  at  the  beginning  and 
the  end  of  the  process  as  a  whole.  Having  made 
these  suppositions  the  next  question  is  what  follows 
if  they  should  be  true.  In  the  first  place,  do  they 
lead  to  any  contradictions  ?  And  in  the  second  place, 
what  if  they  do  ? 


120  USE  OF  WORDS  IN  REASONING        part  i 

The  kind  of  contradiction  they  lead  to  is  the  same 
that  we  encountered  at  the  end  of  hist  chapter  in 
speaking  of  causation  ;  the  kind  that  attaches  im- 
partially to  all  attempts  to  understand  a  process 
which  is  admitted  to  be  continuous.  On  account  of 
its  continuity  we  can  only  understand  it  so  far  as  we 
can  be  content  to  leave  our  understanding  of  it 
incomplete.  The  effort  to  understand  it  involves  an 
artificial  separation  of  it  into  parts,  })oth  successive 
and  side  by  side.  Just  as  with  causation,  so  with 
reasoning — if  it  be  also  continuous — we  cannot  ol)serve 
its  structure  or  composition  unless  we  pick  it  to  pieces 
and  thus  violate  its  unity,  thereby  doing  it  some 
injustice.  And  in  both  cases  the  only  correction 
possible  lies  in  our  remembering  this  defect  as  a  source 
of  error,  and  so  learning  where  to  look  for  the  points 
at  which  correction  may  presumably  be  required  and 
applied. 

Now,  some  help  may  be  got  perhaps  from  remem- 
bering that  the  inquiry  for  a  definition  of  reasonino- 
is  the  attempt  to  discover  its  essence.  For  then,  if 
we  accept  the  modern  view  of  the  nature  of  essence,^ 
we  can  agree  with  both  sides  in  this  otherwise  endless 
dispute.  Since  all  distinction  is  purely  an  affair  of 
purpose,  we  find  no  difficulty  in  admitting  that  there 
are  purposes  for  which  we  are  bound  to  make  this 
particular  distinction  artificially  firm  and  clear ;  and 
at  the  same  time  we  need  have  no  difficulty  in  find- 
ing another  purpose  which  is  better  served  by  the 
consistent  admission  that,  for  all  we  know,  instinct 
and  reason  may  difter  only  in  such  ways  that  they 
are  essentially  one.  The  contrast  is  between  the 
purposes  of  the  psychologist  and  those  of  the  logician, 

*  See  p.  167. 


CH.  iv,§25     REASONING  AND  JUDGMENT  121 

and  we  may  find  that  what  is  a  difficulty  from  one 
of  these  points  of  view  is  only  a  relief  when  seen 
from  the  other.  For  while  the  former  has  to  explain 
the  distinction  between  reasoning  and  judgment,  and 
has  therefore  to  do  each  notion  this  kind  of  justified 
injustice,  the  logician  is  free  from  the  need  of  attempt- 
ing any  such  task.  His  business  is,  not  to  classify 
mental  operations  so  as  to  emphasise  their  points  of 
difference,  but  only  to  examine  them  so  far  as  that 
helps  him  to  see  the  nature  and  sources  of  error.  The 
problem  is,  no  doubt,  set  to  him  at  first  as  the  inquiry 
into  the  difference  between  good  and  bad  reasoning, 
l)ut  if  his  solution  of  it  extends  a  little  further  than 
to  reasoning  '  in  the  proper  sense  of  the  term,'  where 
is  the  harm  of  that  ?  His  account  of  the  nature  of 
error  is  not  necessarily  or  intentionally  restricted  to 
errors  in  reasoning  as  distinct  from  errors  in  simple 
judgment;  the  restriction  to  reasoning  is,  for  the 
logician,  only  an  accident,  or  a  way  of  starting  the 
incjuiry  at  that  end  of  the  scale  which  is  best  open  to 
observation.  There  is  no  loss,  but  rather  a  gain,  if 
we  are  afterwards  led  to  think  that  the  sources  of 
error  are  the  same  in  the  most  deliberate  and  the 
least  deliberate  judgments,  the  same  for  the  beast  and 
the  man.  If  it  be  so,  we  shall  extend  our  insight 
into  the  w^orking  of  higher  and  lower  minds  than  our 
own,  and  some  of  the  apparently  miraculous  character 
will  disappear  both  from  their  wisdom  and  their  folly. 


8  25. — The  AVeak  Points  of  Reasoning  or 

Judgment 

Any  piece  of  reasoning,  we  have  seen, — keeping 
in  view  first  only  those  cases  which  every  one  would 


^ 


1  99 

X   mJ  ^ 


USE  OF   WORDS  TX  REASONING        i-akti 


allow  to  1)0  reasoning, — is  syllogistic  to  this  extent, 
that    it    involves   both    T)revious   fjeneral    knowledire 
and   the  present  conception  of  particular  facts  under 
general   names.       If  the  desire  for  accuracy  of  con- 
clusion drives  us  to  analyse  further   in  a  given  case, 
still    the  same    two  elements  appear  at  every  step. 
Our  major  premiss  being  (questioned  we  attempt  to 
show  it  as  an  interpretation  (in  the  light  of  previous 
general  knowledge)  of  particular  facts  observed  (and 
conc^eived     under    general    names).       If   our    minor 
premiss    comes    under   suspicion   w^e  seek   to   justify 
the  predicate  M  by  exactly  the  same   procedure  ;  S, 
we  contend,  has  certain  features  (des(nibed  again   by 
general  names)  which  give  it  a  rii:;ht  (here   i)revious 
general  knowledge  comes  in)  to  a  place  in  the  class 
M.     Accordingly   it  appears  that  all   criticism  of  a 
reasoned  judgment  can  avail  itself  of  two  points  of 
attack,  one  or  both  of  which  may    be  followed  uj) ; 
and  in  following  them  up,  however  far  we  pursue  the 
inquiry,    the  same  tw^o  lines  of  objection   are  open 
until   w^e  can  be  satisfied  to  close   them.     Thus   the 
risks  in  deliberate  reasoning  are  due  to  (1)  defects  in 
our  previous  general  knowledge,  and  (2)  defects  in 
our  conception  of  the  particular  fact  or  set  of  facts 
from   which  the  conclusion  seems  to  follow.      Even 
the  most  emotional  sources  of  error — hope,  or  fear, 
or  love,  or  hatred — can  only  take  effect  in  these  tw^o 
ways.     Gross  errors  may  be  accounted  for  by  gross 
defects  of  either  kind,  but  when  we  consider  the  kind 
of  error  that  is  really  troublesome  to  detect  and  still 
more  difficult  to  conquer  permanently,  we  may  trace 
it  to  the  insufficient  analysis  (past  or   present)  of 
some  fact  or  fticts  observed,— a  defect  which  has  for 
its  most  intelligible  cause  the  power  of  general  names 


CH.  iv,^25     REASONING  AND  JUDGMENT  123 

to  hide  individual  differences  whose  real  importance 
happens  not  to  be  seen. 

Now  if  we  look  at  the  judgments  of  the  human 
intuitive  seer  on  the  one  hand,  or  the  dog  on  the 
other,  what  ground  have  we  to  assume  that  these 
two  sources  of  error  have  suddenly  disappeared  in 
favour  of  others  to  which  we  have  no  clue  ?  What 
has  disappeared,  at  least  explicitly,  is  the  use  of 
general  names ;  and  of  reasoning  w^ithout  explicit 
general  names  we  all  have  plenty  of  experience  in 
person.  The  reasonings  in  a  game  of  chess,  for 
instance,  are  largely  of  this  nature ;  we  have  a 
general  name  for  the  situation  *  in  check,'  *  stale- 
mate/ and  so  on,  but  there  are  dozens  of  other 
recurring  situations, —for  example,  in  an  end-game 
with  kings  and  pawns  only — where  general  names 
ha\e  not  been  invented  and  wdiere  they  would  be  of 
great  use  to  a  beginner.  But  the  errors  we  commit 
in  the  absence  of  general  names  are  just  the  same 
as  if  we  had  applied  a  general  name  to  a  situation 
which  did  not  fully  deserve  it.  What  other  error, 
in  fact,  can  there  be  than  either  (1)  that  we  over- 
look or  over-emphasise  some  detail  in  the  situation, 
and  so  sum  it  up  under  a  false  general  conception,  or 
(2)  that  our  previous  experience  is  insufficient  to 
show  us  clearly  the  meaning  —  the  inevitable  con- 
sequences —  of  a  given  situation  ?  And  the  same 
holds  not  only  in  games  but  in  all  the  most  serious 
business  of  life.  We  are  always  having  to  deal  with 
situations  in  the  light  of  our  previous  experience, 
and  w^e  often  have  to  do  this  without  any  accepted 
general  names  which  can  be  used  to  sum  up  the 
situation  as  a  whole. 

Similarly  with  the  scalded  dog  who  dreads  cold 


124 


USE  OF  WORDS  IN  REASONING        part  i 


water,  or  the  stupid  dog  who  learns  from  experience 
more  slowly  or  more  faultily  than  others.  He  too 
sums  up  a  situation  and  its  meaning,  and  in  doing 
so  he  overlooks  essential  details,  and  gives  undue 
weight  to  accidental  ones,  just  as  we  all  do  when 
we  lose  a  game  of  chess,  or  when  we  are  tricked  l)y 
a  conjurer,  or  when  we  draw  any  false  conclusion 
however  deliberately.  Fully  admitting  that  we 
cannot  quite  get  inside  a  dog's  mind,  and  that  our 
retrospection  of  our  own  hurried  or  inarticulate  judg- 
ment is  to  a  great  extent  impossible  or  delusive, 
may  we  not  still  expect  that  the  mere  presence  or 
absence  of  explicit  language  can  make  no  more 
difference  to  the  sources  of  error  than  has  here  been 
suggested  ?  If  otherwise,  where  are  we  to  look  for 
any  explanation  of  the  ways  in  which  a  poet  or 
an  animal  commits  an  error  of  judgment  ?  None,  I 
believe,'  has  ever  been  offered  by  those  who  claim 
that  reasoning  and  instinct  are  essentially  different 
things.  Instinct  is  a  wonderful  thing  when  it  leads 
us  right,  but  there  is  less  occasion  for  blank  uncom- 
prehending wonder  when  instinct  leads  us  wronir. 


§  26. — Some  Objections  Considered 

Nevertheless  a  view  of  this  kind  cannot  expect, 
and  need  not  desire,  to  have  an  easy  time  or  en- 
counter no  opposition.  Arrayed  against  it  there  are 
on  the  one  hand  the  frankly  abstract  and  disjointed 
conception  of  reasoning  which  is  encouraged  by 
Formal  Logic,  and  on  the  other  hand  the  sturdy 
common -sense  view  which  is  inclined  to  suspect 
philosophy  of  causing  needless  inconvenience,  or 
worse,  through  tampering  with  valuable  distinctions. 


CH.iv,§26     REASONING  AND  JUDGMENT  125 

Our  virtuous  horror  of  casuistry  often  overshoots  its 
mark  and  suspects  all  refinements  of  thought  im- 
partially, the  useful  ones  included.  One  may  guess 
what  Dr.  Johnson  would  have  found  to  say  about 
Darwin's  views,  or  Whately  about  Bosanquet's  Logic. 
It  is  always  tempting  to  end  one  of  these  discussions 
by  the  ultimatum  that  ''  After  all,  X  is  X,  and  Y  is  Y, 
and  there's  an  end  on't." 

As  to  this  latter  line  of  objection,  however,  there 
is  really  no  need  to  suppose  that  in  our  suggested 
identification  of  judgment  and  reasoning  we  are 
running  any  risk  of  doing  away  with  the  notion  of 
reasoning  altogether.  We  need  no  more  do  this 
than  the  Darwinians  do  away  with  the  word 
'species,'  or  than  our  common  recognition  of  the 
fact  that  man's  growth  is  gradual  does  away  with 
the  words  *  child  '  and  '  man.'  It  is  one  thing  to 
explain  a  word  as  having  a  value  only  for  certain 
limited  purposes,  and  quite  another  to  condemn  the 
word  as  useless.  There  are  times  when  we  need  to 
speak  rather  of  accomplished  facts  than  of  their 
unfinished  stages,  but  the  unfinished  stages  exist 
nevertheless,  and  a  view  of  them  is  for  some  purposes 
desirable. 

And  secondly,  the  chief  purpose  for  which  this 
kind  of  view  is  wanted  is  that  of  helping  us  to 
trace  to  their  source  those  errors  of  reasonin^y  which 
are  subtle  and  therefore  effective.  The  fact  that 
those  who  are  much  under  the  influence  of  Formal 
Logic  dislike  our  view  is  no  doubt  regrettable,  but 
neither  unnatural  nor  incapable  of  change.  Just  so 
the  old  order  must  always  dislike  and  distrust  the 
new,  regarding  it  as  little  better  than  chaos.  Our 
counter-claim  is  that  the  old  machinery  is  cramped 


126 


USE  OF  WORDS  IX  REASONING        part  i 


and  rusty,  and  the  old  view  of  the  faults  of  reason- 
ing clogged   and   hindered  at  every  turn  by  debris 
that  is  better  removed.     Under  the  traditional  system 
only  the  clumsier  kinds  of  fallacy  can  be  taken  into 
account, — only  the  kinds  that  require  least    logical 
insight  for  their  avoidance.     For  if  it  is  reckoned  (as 
by  Whately)  outside  the  province  of  Logic  ever  to 
raise    the    question    whether   the    data    of   a   given 
inference  are  true,   the  mental   process  by  which   a 
false  inference  is  taken  for  true  remains  inexplicable ; 
we  have  no  account  to  give  of  it  except  that  some 
rule  of  Logic  has  been   transgressed.     And  then  the 
inquiring   spirit   naturally    wants  to   know   whether 
perhaps  the  rules  do  not,  after  all,  deserve  a  little 
judicious  transgression.     At  any  rate  it  is  clear  that 
a  Logic  which  restricts  itself  to  the  supposition  that 
facts  are  always  correctly  conceived  has  an  extremely 
limited  range  of  utility.     What  the  less  formal  view 
of  the    nature  of   reasoning  does  is  to  lead    us   to 
look    for   the    weak   points  of  an   argument  in   the 
conception   of   some   fact   on    which    the   conclusion 
directly   or   indirectly    turns, — directly    when    it    is 
found  in  the  minor  premiss,  and  indirectly  when  it 
is  among  the  supports    of  the   major    premiss  (or   a 
part  of  it), — however  far  back  that  search  may  lead 
us.     The  contention  is  that  to  explain  the  existence 
of  error  (other  than  the  comparatively  simple  error 
due  to  careless  interpretation  of  sentence-forms)  in  any 
conclusion,  whether  commonly  called  'reasoned'  or 
not,  there  must  be  faulty  conception  of  fact  at  some 
earlier  stage  of  the  train  of  thought  which  ends  in 
that  conclusion.     It  can  be  so  traced  in  cases  where 
the  reasoning  is  deliberate ;  it  can  often  be  suspected 
with  some  justification  in  other  cases  where  language 


CH.  iv,§26     REASONING  AND  JUDGMENT 


127 


is  not  expressly  used ;  and  what  risk  lies  in  suspect- 
ing its  existence  in  all  cases  whether  of  the  quickest 
or  the  dullest  erroneous  thought  no  one  has  yet 
tried  to  tell  us.  Indeed,  how  is  it  possible  to  con- 
ceive error  as  arising  ex  nihilo  f 

ileanwhile,   we  claim   that   we  can   in   this   way 
begin  to  understand  how  faults  in  reasoning  occur,— 
a  problem  which  Formal  Logic  virtually  ignores,  and 
whi<th  calls  for  solution  most  in   those  cases  which 
Formal  Logic  leaves  most  out  of  si<j:ht, — the  reasonino-s 
where  some  care  is  taken  and  where  the  faulty  con- 
elusion  wears  an  appearance  of  correctness.      These 
are  the  cases  where  Logic  is  specially  wanted ;  if  it 
declines  to  deal  with  them  on  the  ground  that  such 
investigations  are  outside  its  province,  we  can  only 
answer  that  it  is  a  thousand  pities  that  its  province 
should  be  restricted  to  such  a  trivial  field.    Especially 
where  Logic  is  called  upon  to  help  in  deciding  between 
different  opinions  backed  by  reasons,  it  must  fail  if 
it  keeps  to  its  old  simple-minded  supercilious  ways. 
It  is  hard  to  convince  an  opponent  at  any  time,  but 
the  only  chance  lies  in  going  along  with  him  as  far 
as  you  can.     If  you  are  content  to  accuse  him  point- 
blank  of  breaking  some  rule  of  the  Syllogism,  or  of 
needing  to  be  reminded  of  the  truth  of  the  abstract 
inductive  canons,   you   will   never   convince  him   of 
error.     The  error,  if  any,  from  which  his  conclusion 
suffers  must  be  traced  to  its  source.     You  must  show 
him  where  and  how  it  arose,  the  defects  of  his  view 
of  the  case,  the  additional  facts  w^iicli  he  has  over- 
looked, and  which  being  added  to  those  he  has  seen 
can  hardly  ])e  denied  to  *  throw  a  new  light  on  the 
circumstances.'     Even  for  this  reason  it  is  a  gain  to 
recognise  that  all  error  is  due  to  a  lack  of  sufficient 


128 


USE  OF  WORDS  IN  REASONING        paiit  i 


light  on  the  facts  observed/  and  that  any  point  in 
dispute  may  be  resolved  into,  or  traced  to,  a  question 
which  of  two  different  descriptions  of  a  piece  of  fact 
is  the  less  inaccurate. 

On  the  other  hand  it  may  be  freely  admitted  that 
arguments  which  raise  no  dispute  as  to  the  soundness 
of  the  conclusion  may  often  come  more  naturally 
under  the  old  conception  of  reasoning  as  a  process  of 
building  a  structure  by  putting  together  isolated 
bricks  of  thought.  Chief  among  these  are,  no  doubt, 
mathematical  reasonings — which,  as  we  have  seen, 
may  be  treated  as  a  class  by  themselves.  But  a 
careful  search  will  also  bring  to  light  a  certain 
proportion  of  other  cases  where  we  get  a  piece  of 
knowledge,  and  then  another  piece  of  knowledge, 
and  then  suddenly  see  that  these  are  premisses  and 
yield  a  logical  conclusion.'-  Such  examples,  however, 
have  little  or  nothing  to  do  with  an  inquiry  into  the 
difference  between  good  and  bad  reasoning.  Con- 
clusions which  no  one  would  dispute,  like  conclusions 
which  every  one  would  reject,  fail  to  illustrate  any 
of  the  real  difficulties  of  the  problem,  and  therefore 
do    not   call  for  refinements  of  explanation.      It  is 

*  In  saying  this  we  are  excluding  all  eases  of  confused  reasoning  or 
judgment  which  involve  a  downright  failure  to  connect  the  evidence  with 
the  conclusion  ;  where,  for  instance,  instead  of  proving  the  disputed 
assertion  you  prove  another  which  is  not  disputed,  or  where  instead  of 
proving  it  you  assume  its  truth  in  some  disguised  form  and  then  deduce 
its  truth  from  that  assumption.  These  are  exceedingly  common  contro- 
versial tricks  or  failures,  and  in  a  work  on  controversy,  rather  than  on  I-ogic, 
they  would  recpiire  treating  at  some  length.  In  the  present  book,  however,' 
there  is  not  much  that  need  be  said  about  them,  except  so  far  as  the  habits 
in  question  vitiate  certain  logical  doctrines.     See  also  §  28. 

'^  Mr.  Bosancjuet  {Essentials  of  Logic,  p.  140)  (quotes  from  Tliackeray 
an  example  which  may  serve  to  illustrate  this  case:  —  *'An  old  Abb.-, 
talking  among  a  party  of  intimate  friends,  hapi>ened  to  say,  ♦  A  priest  has 
strange  exi)eriences  ;  why,  ladies,  my  first  |)enitent  was  a  munlerer.'  U])on 
this  the  principal  nobleman  of  the  neighbourhood  enters  the  room  :  '  Ah, 
Abb«^,  here  you  are  ;  do  you  know,  ladies,  I  was  the  Abbe's  first  penitent] 
and  I  promise  you  my  confession  astonished  him.'  " 


CH.  IV,  §  27     REASONING  AND  JUDGMENT  ]  29 

chiefly  when  we  keep  in  view  arguments  where  the 
faults  of  the  conclusion  are  not  easily  discovered  that 
It  becomes  important  to  trace  the  error  to  its  source 
in  earlier  stages  of  the  judgment. 

§  27. — Thk  False  Duality  of  the  Premisses 

The   unity  behind  the   apparent   duality  of  the 
sources  of  error  in  reasoning  may,  however,  best  be 
seen  by  recognising  that  questions  of  fact  can  only 
roughly  be  separated  from  questions  of  theory.     This 
will  come  out  more  plainly  in  Part  II.,  which  deals 
specially  with  statements  of  fact  and  the  difficulties 
they  encounter  in  achieving  accuracy  and  escaping 
vagueness;    but  at  several  points  already  we  have 
had  glimpses  of  the  nature  of  the  relation  between 
theory  and  fact,— a  complex  relation  of  warfare  and 
mutual  aid.      Tlie  struggle  between  them  is  one  of 
the  fundamental  troubles  of  human  thought,  and  our 
efforts  to  deal  with  it  are  precisely  co-extensive  with 
our  efforts  to  gain  increased  knowledge  of  any  kind. 
Every  piece  of  supposed  new  fact  we  discover  has  in 
the  first  place  to  stand  against  the  criticism  of  our 
previous  theories  as  to  what  is  possible,  and  in  the 
second    place    whatever    part    of    it    survives    this 
criticism   reacts   upon    the   store   of  general    know- 
ledge itself;    some  generalisations  are  confirmed  by 
It,  wliile  others  are  modified  or  upset.     One  aspect  of 
this  rivalry  claimed  our  notice  in  chap.   i.  (p.   43), 
where  we  saw  the  effect  of  an  extension  of  knowledge 
of  particular  cases  in  raising  a  question  whether  a 
familiar  definition   ought   to   be   widened,    and   the 
consequent   eff'ect   upon   a   rule  which   needs   inter- 
pretation.     It  matters  not  whether  the  rule  be  an 


130 


USE  OF  WORDS  IN  REASONING        part  i 


attempt  to  state  the  universal  connection  between 
X  and  Y — as  in  the  half-truth  that  all  swans  are 
white — or  on  the  other  hand  a  rule  laid  down  for 
some  kind  of  human  convenience,  such  as  an  Act  of 
Parliament  or  an  agreement  of  international  law. 
Generalisation  of  any  kind,  in  so  far  as  it  aims  at 
precision,  is  lial)le  to  this  increase  of  definiteness 
through  the  consideration  of  doubtful  instances. 
For  whether  the  rule  be  enlarged  so  as  to  take  in 
the  doubtful  instance,  or  limited  so  as  to  exclude 
it,  in  either  case  both  the  rule  and  the  instance 
have  moved  forward  a  step  towards  more  precise 
conception. 

Another  aspect  of  the  same  relation  between  fact 
and  theory  is  seen  in  the  doctrine  (p.  20)  that  the 
meaning  of  any  general  statement  lies  in  its  applica- 
tion to  particular  cases.  The  possil)le  facts  to  which 
a  theory  refers  are  nothing  else  than  the  possible 
applications  of  a  general  statement.  Tliey  are  at 
once  the  matter  (or  meaning)  of  the  theory,  and, 
by  means  of  the  doul)tful  instances,  the  force 
which  moulds  it  into  better  and  clearer  sliape.  By 
checkin<i  here  and  enlar<jjin^  there  they  are  alwavs 
pulling  down  the  less  secure  parts  of  the  structure, 
and  rebuilding  with  better  material. 

In  chap,  ii.,  and  again  in  chap.  iii.  (pp.  98,  99), 
we  reached  a  rather  more  ditticult  view  of  the  way 
in  which  fact  and  theory  (or  minor  and  major 
premiss)  are  bound  up  together,  so  that  the 
question  whether  the  '  fact  produced '  is  true, 
and  the  question  whether  it  is  revelant,  can  hardly 
be  called  separate  questions.  We  saw  that,  in  the 
case  of  the  more  disputable  conclusions,  these  two 
questions  tend  to  become  one.     Or  if  we  still  prefer 


cH.iv,^28     REASONING  AND  JUDGMENT  131 

to  regard  them  as  two  questions,  at  least  we  have 
to  admit  that  neither  of  them  can  be  answered 
carefully  without  also  answering  the  other.  In 
order  to  judge  what  caused  what,  in  a  given 
occurrence,  it  is  necessary  that  our  facts  should  be 
correctly  observed  and  conceived;  but  since  our 
conception  of  any  fact  is  also  dependent  on  the 
state  of  our  general  knowledge,  progress  in  either 
of  the  two  lines  of  inquiry  involves  and  demands  pro- 
gress in  both.  The  more  difficult  it  is  to  make  sure 
whether  a  fact  produced  has  been  sufficiently  analysed 
into  its  details,  the  more  difficult  it  is  to  locate  the 
fault  of  the  reasoning  in  either  premiss  taken  by 
itself  The  grosser  the  faults  of  an  argument  are, 
the  more  easily  can  we  put  our  finger  either  on  the 
false  fact  or  the  false  generalisation. 


§  28. — Syllogism  and  Fetitio  Phincipii 

A  further  view  of  this  truth  may  be  obtained  by 
a  glance  at  the  old  puzzle  whether  the  Syllogism 
involves  a  petitio  principii^  That  a  given  syllogism 
may,  l)ut  need  not,  beg  the  question  whether  its 
conclusion  is  true,  is  now^  admitted  by  every  logician 

'  A  translation  of  tlie  i)lirase  petitio  principii,  or  '  bcg«riiig  the  (luestion,' 
may  l.o  given  in  several  ways,  perhaps  the  simplest  being  'suiiei.titious 
assumption  ol"  a  truth  you  are  pretending  to  j.rove.'  But  this  of  course 
«l(«s  nut  carry  us  lar  in  tracing  the  trick  into  its  more  effective  forms,  for 
the  ellectiveness  of  any  trick  (lei»en(Js  on  its  assuming  a  good  disguise  ;  and 
thus  the  inherent  tendency  of  tricks  is  to  depart  from  the  recognised  type  so 
far  iis  appearance  goes,  in  the  hope  of  eluding  detection.  And  since  arguing 
•y  nieans  of  exj.resseci  syllogisms  is  widely  discredited  nowadays,  qucstion- 
I'egging  chiefly  occurs  where  nothing  like  formal  proof  is  set  out,  and  where 
It  imght  hotter  he  called  the  surreptitious  assumjition  that  a  doubt  is  solved 
tli.in  that  a  truth  is  proved,— since  the  latter  expression  seems  to  point  too 
exclusively  to  the  case  where  an  explicit  conclusion  is  hacked  by  explicit 
reasons. 

^^  ith  this  confusion  or  trick  we  have  already  made  some  ac(iuaintance  in 
two  ol  Its  commonest  forms  :  the  attenipt  to  satisfy  a  request  for  a  dehnition 
hy  m-ans  of  a  mere  translation,  and  the  attempt  to  defend  a  shaky  assertion 
l>y  making  it  purely  abstract. 


132  VSE  OF  WORDS  IN  REASONING        parti 

who  understands  the  difference  between  begging  a 
question  and  raising  one.  The  two  operations  are, 
no  doubt,  easily  confused ;  but  all  that  is  necessary 
to  keep  them  separate  at  least  in  idea  is  to  rememl)er 
that  no  assumption  amounts  to  question -begging  un- 
less it  is  surreptitious.  A  syllogism  begs  the  question 
only  where  the  pretence  is  made  that  an  unadmitted 
premiss  is  (or  must  be)  admitted.  In  the  absence  of 
this  pretence  there  is  no  question-begging,  for  then 
we  are  either  openly  asking  whether  the  premisses 
are  admitted— and  if  they  are  not,  the  question  at 
issue  changes— or  else  we  are  openly  assuming  the 
truth  of  the  premisses  *  for  the  sake  of  argument,' 
and  leaving  perfectly  open  the  question  whether  they 
are  true  as  a  matter  of  fact.  Open  assumption  is  not 
only  le^ntimate,  but  necessary  for  all  progress  of  know- 
ledf^e  ;  ^  to  assume  openly  the  truth  of  a  statement  is 
properly  no  more  than  to  ask  whether  it  is  true,— to 
guess  in  the  hope  of  verifying,  or  to  state  in  the  hope 
of  disproving.  In  the  legitimate  use  of  reflective 
syllogism  the  reasoner  would  be  the  last  to  deny 
that'^the  premisses  taken  together  are  only  a  re- 
statement of  the  conclusion  in  an  expanded  form. 
No  claim  inconsistent  with  this  admission  is  made 
for  them.  And  the  re -statement  has  an  obvious^ 
purpose.  By  thus  breaking  up  the  conclusion  into 
rule  and  application  we  do  two  things:  we  lay  it 
open  to  a  more  definite  attack  than  l)efore,  and  we 
make  an  attempt  in  the  direction  of  showing  causa- 
tion behind  it. 

1  otherwise  whoever  disliked  a  pvcn  conchision  could  at  once  reduce  to 
futility  the  best  possible  reasons  tor  accepting  it  ;  indeed,  the  better  they 
were  the  more  they  would  be  oi>en  to  the  char{j;e  of  .luestion-begging  in  thi^ 
seme  Only  a  iK)or  kind  of  Logic  could  be  satisfied  to  make  our  own 
nrefereuce  for  or  against  a  conclusion  the  test  of  the  force  of  the  rea^ion* 
given  for  it.     Not  by  this  method  has  knowledge  ever  advanced. 


133 


CH.  IV,  ^  28     REASONING  AND  JUDGMENT  \ 

As  admitted  already,  a  given  syllogism  may 
contain  an  attempt  to  beg  the  question.  But  it  is 
difficult  to  conceive  any  examples  of  this  trick  that 
do  not  depend  on  an  ambiguity  of  the  middle  term. 
For  in  order  to  beg  the  question,  the  premisses  must 
of  course  seem  true, — else  the  question  as  to  their 
truth  might  arise,  and  that  (we  are  now  supposing) 
is  the  very  point  which  is  to  be  slurred  over  as  much 
as  possible.  And  the  chief  occasion  on  which 
premisses  seem  true  when  the  reasoning  is  unsound 
is  where  each  premiss  taken  by  itself  is  true  in  some 
sense,  but  the  two  taken  together  are  false.  The 
statement,  for  instance,  that  money  is  wealth  is  true 
enougli  if  taken  loosely  and  not  connected  with  the 
maxim  that  the  accumulation  of  wealth  in  a  country 
is  an  economical  gain.  But  to  take  these  two  state- 
ments together  and  use  them  in  support  of  the  '  Mer- 
cantile System '  is  to  pass  too  lightly  over  the  question 
whether  money  is  wealth  in  just  the  sense  required. 

On  this  account  it  is  only  in  arguments  of  the 
simplest  and  least  debatable  kind  that  the  reliance  on 
syllogistic  proof  is  7iot  a  suspicious  circumstance. 
The  more  arguable  a  question  is,  the  more  we  may 
expect  to  find  that  any  apparently  simple  syllogistic 
solution  of  it  contains  an  ambiguity  of  the  middle 
term.  In  such  cases  the  term  M  is  a  clumsy  or 
superficial  description  to  apply  to  S,  a  word  which 
liides  the  real  complication  of  S's  nature  under  a 
misleading  verbal  simplicity.  S  is  M,  in  a  sense,  else 
the  false  conclusion  would  not  seem  true  ;  but  it  is 
also  in  some  sense  not  M,  else  the  dispute  would  not 
have  arisen.  The  question  remains  whether  S  is  or 
is  not  M  in  just  that  sense  in  which  it  is  true  that 
from    ]M    follows   P.      There    is    only   one   way   to 


134 


USE  OF  WORDS  IN  REASONING        part  r 


approach  the  settlement  of  such  a  question,  and  that 
is  to  enter  upon  an  inquiry  into  the  details  of  the  fact 
S,  and  at  the  same  time  into  the  precise  interpreta- 
tion of  the  law  that  from  M  follows  P. 

It  appears,  then,  that  a  syllogism  only  escapes 
involving  petitio  j^'t^iT^cijni  when  the  question  is  left 
open  whether  M  is  ambiguous.  Actual  question - 
])egging  under  cover  of  the  syllogistic  form  is  a 
special  result  of  neglect  of  the  risk  of  ambiguity  in 
the  middle  term.  To  neglect  this  risk  is  to  ignore 
the  subtle  change  that  comes  over  the  meaning  of 
two  statements  when  they  are  put  together  and  re- 
viewed in  the  light  of  a  particular  conclusion  which 
they  are  supposed  to  guarantee.  The  major  premiss 
or  statement  of  theory,  and  the  minor  premiss  or 
statement  of  fact,  determine  each  the  meaning  of  the 
other ;  and  Ijy  ignoring  this  we  may  surreptitiously 
claim  truth  for  a  proposition  which  is  ftilse. 

The  effect  of  each  premiss  on  the  other  is  to  make 
a  vague  meaning  more  definite.  When  the  general 
rule  '  All  iVI  are  P '  is  interpreted  so  as  to  include  the 
case  S,  it  takes  on  a  more  definite  meaning  than  it 
had  while  this  application  of  it  was  not  clearly  fore- 
seen ;  and  its  truth  becomes  accordingly  more  difficult 
to  establish.  In  the  same  way  the  statement  of  fact 
that  S  is  M  loses  some  of  its  vagueness  and  irre- 
sponsibility when  M  is  expressly  defined  as  the  M 
which  indicates  P.  Any  statement  whether  of  fact 
or  of  theory  gains  in  definiteness,  and  so  loses  in 
easiness  of  acceptance,  by  being  tied  down  to  a 
particular  interpretation.  In  this  way  statements 
which,  taken  in  isolation  from  each  other,  legitimately 
pass  for  true,  may  when  combined  as  premisses  be 
false  and  so  support  a  false  conclusion. 


CH.iv,§29     REASONING  AND  JUDGMENT  135 

§  29. — Transition  to  Part  II 

The  conception  of  theory  and  fact  as  each  de- 
pendent   on    the    other   presents,   of    course,   some 
difficulty, — of  a  merely  verbal  kind,  however, — since 
we  are  too  apt  to  think  of  the  acceptance  of  a  fact, 
or  of  a  theory,   as  a  sudden  act  once  for  all   per- 
formed, instead  of  as  merely  part  of  an  unfinished 
movement  of  thought.     It  is  only  where  X  is  com- 
plete before  Y  comes  into  existence  that  the  axiom 
that  Cause  precedes  Eff*ect  can  be  appealed  to  as  for- 
bidding the  interdependence  of  X  and  Y;  two  things 
which  grow  simultaneously  may  help  forward  each 
other  s  growth,  as  with  the  widening  leak  in  a  dam 
and  the  trickle  or  rush  of  the  water  through  it.     In 
such  cases,  to  study  the  growth  of  the  one  feature  is 
also  to  study  the  growth  of  the  other,  and  it  scarcely 
matters  which  w^e  choose  expressly  for  investigation. 
Part  II.  will  therefore  begin  with  the  inquiry  what 
is  involved  in  the  process  of  predication,  or  state- 
ment of  fact ;  and  the  discussion  of  certain  natural 
errors  and  half-truths  which  are  always  in  danger  of 
being  trusted  beyond  their  legitimate  use  will  lead 
us    to    a    fuller    understanding    of    the   nature    of 
am])iguity  and  its  remedy,   definition.      Reasoning, 
it  has  here  been  suggested,  is  not  best  explained  as 
a   mechanical  placing  together  of  premisses  out  of 
which  a  conclusion  is  pressed,  nor  even  as  a  marshal- 
ling of  undeniable  facts  out  of  which  a  theory  is  built 
by  any  facile  process  of  "  dropping  out  of  sight  their 
accidental  features."     It  is  rather  a  process  of  letting 
a  half- formed  judgment  grow,   in  the  bracing  and 
cleansing  air  of  criticism  directed  upon  the  supposed 
facts  appealed  to.     The  whole  purpose  of  repeating 


136 


USE  OF  WORDS  IN  IlEASONIXG        part  r 


en.  IV,  §  29     REASONING  AND  JUDGMENT 


137 


1'; 


ft; 


observations  or  experiments  is  to  allay  the  doubt 
whether  the  *  facts  '  were  not  somehow  misconceived. 
That  is  w^hy  the  search  for  a  definition  is  not  merely 
a  game  for  quil^blers  and  the  *  choppers  of  Logic '  to 
play  at,  but  is  the  most  important  factor  in  all 
attempts  to  guard  our  reasoned  judgments  from  error, 
whether  in  scientific  discovery  or  in  the  affairs  of 
daily  life.  And  that  is  why  it  is  necessary  for  the 
student  of  Logic  to  get  as  true  a  conception  as 
possible  of  the  nature  of  this  process  and  of  the 
nature  of  amlnguity — the  defect  which  the  search  for 
a  definition  tries  to  remedy.  We  have  seen  that  all 
false  judgment  involves  false  conception  of  some  fact 
or  facts  ;  that  the  kind  of  fiilse  conception  which  is 
least  easily  avoided  is  where  slightly  too  much  or  too 
little  importance  is  given  to  one  of  the  circumstances 
present  in  a  complex  fact— for  instance  where  the 
intelligent  foreigner  only  slightly  exaggerates  the 
less  respectable  motives  of  England's  foreign  policy, 
or  only  slightly  underrates  whatever  other  motives 
are  concerned  in  it.  The  farther  we  get  from  the 
lower  end  of  the  scale,  where  the  falsity  of  the 
explanation  is  gross  and  obvious,  the  more  evidently 
the  fault  consists  in  giving  a  wrong  name  to  a 
complex  fact,  or  in  conceiving  a  complex  fact  too 
simply.  In  a  fact  containing  the  elements  X  and  Z, 
the  X  element  may  be  singled  out  and  noticed  un- 
deservedly; the  fact  as  a  whole  is  taken  as  being 
more  simply  X  than  it  is,  and  thus  the  weakness  of 
the  explanation  consists  in  forgetting  one  of  the 
subtle  ways  in  which  a  name  may  be  wronglv 
applied.  Even  low  down  on  the  scale  this  account 
of  the  fault  begins  to  be  intelligible,  though  it  is 
there  less  clearly  appropriate.     For  instance,  where 


the  child  imagines  that  the  watch  was  opened  by 
1  blowing  on  it,  we  should  naturally  say  that  he 
totally  mistakes  the  nature  of  the  occurrence, — puts 
down  the  eftect  to  one  thing  wdiile  it  was  really  due 
to  another.  But  it  would  also  be  strictly  correct  to 
.say  that  he  has  a  complex  fact  before  him,  consisting 
(among  other  things)  of  the  obvious  blowdng  and  the 
less  obvious  pressure  of  the  finger  on  the  spring,  and 
that  he  conceives  this  complex  fact  too  simply 
through  overlooking  one  of  its  details.  Fortunately, 
however,  w^e  need  not  compel  ourselves,  in  cases  so 
low  on  the  scale,  to  decide  between  these  two  ways 
of  viewing  them.  It  is  enough  to  recognise  that  the 
more  nearly  true  a  false  explanation  is  the  more 
naturally  it  may  be  viewed  as  a  case  of  false  balance 
between  more  and  less  obvious  factors  in  a  complex 
fact. 

To  Logic,  therefore,  the  need  of  recognising  faulty 
description  as  a  highly  practical  danger,  and  the 
demand  for  strict  definition  as  liable  to  become  of 
extreme  importance  at  any  moment,  is,  as  we  shall 
see,  of  the  most  far-reaching  kind.  With  this 
recognition  comes  a  radical  change  in  our  view  of 
the  nature  and  effects  of  amlnguity.  It  is  no  longer 
a  merely  academic  1)lemish  which  may  be  put  out  of 
consideration  as  of  small  practical  importance  owing 
to  its  rarity.  Definition  and  Classification  are  no 
longer  subjects  which  can  l)e  perfunctorily  treated, 
even  in  a  textbook.  Discussion  of  them  becomes 
rather  the  core  of  any  logical  teaching  which  aims 
chiefly  at  understanding  how  faults  in  a  reasoning 
process  arise  and  what  makes  them  most  effective. 


PART  II 


DESCRIPTION  AND  AMBIGUITY 


CHAPTER  V 


description,  in  general 

§  30. — Description  involves  the  Use  of 

Class-Names 

Since  incorrect  reasoning  involves  incorrect  descrip- 
tion ^  of  the  facts  from  which  the  reasoning  proceeds, 
it  follows  that  in  discussing  generally  the  ways  in 
which  facts  come  to  be  falsely  described,  or  miscon- 
ceived, we  are  directly  approaching  the  central 
problem  of  Logic.  Now  among  the  sources  of  mis- 
conception of  fact  the  (tacit  or  express)  use  of  words 
admittedly  holds  an  important  place,  and  is  at  the 
same  time  the  only  one  that  at  present  seems  to 
allow  of  general  treatment.  The  precise  effect  of  our 
other  and  less  avoidable  mental  or  spiritual  dis- 
abilities is  to  some  extent — owing  to  those  disabilities 
themselves — beyond  our  ken ;  and  even  where  it  is 
not  so  it  varies  too  much  from  person  to  person  to 
come  within  the  scope  of  the  present  inquiry,  which 
gladly  accepts  to  that  extent  the  traditional  limita- 

^  The  word  'describe'  is  here  used  to  include  'conceive.'  To  con- 
ceive a  fact  is  to  describe  it  tacitly ;  to  describe  a  fact  is  to  give 
expression  to  a  conception  already  formed.  We  may  therefore  use  either 
vord  indifferently,  except  where  there  is  any  need  to  distinguish  between 
express  and  tacit  reasoning.  Again,  the  distinction  generally  made  between 
description  and  explanation  is  here  neglected  as  irrelevant,  since  description 
is  incomplete  in  so  far  as  it  is  not  explanatory. 


142 


USE  OF  WORDS  IN  REASONING       part  ii 


en.  V,  §  30      DESCRIPTION,  IN  GENERAL 


143 


tions  of  Logic.  We  may  in  the  meantime  be  content 
with  a  less  hopeless  branch  of  knowledge.  The  snares 
and  shortcomings  of  language — the  price  we  have  to 
pay  for  the  convenience  of  using  words — these  are 
subjects  more  or  less  forced  upon  the  notice  of  every- 
body at  times,  and  they  have  rightly  been  recognised 
as  important  ever  since  Logic  first  turned  attention 
to  them.  What  we  are  now  to  do  is  to  find  fault 
with  some  of  the  leading  generalisations  about  the 
nature  of  description  which  have  been  reached  by 
common  sense  and  adopted  with  insuflicient  criticism 
by  the  traditional  Logic. 

The  most  elementary  truth  about  description  is 
that  it  cannot  be  performed  otherwise  than  either  by 
means  of  class-names — also  called  in  Logic  *  general 
names '  ^ — or  by  names  which  though  not  commonly 
used  as  class-names  yet  take  on  the  characteristics 
of  class-names  when  they  are  used  to  describe.  To 
describe  anything  is  to  make  what  is  technically 
called  a  'predication'  (or  predicative  assertion) 
about  it ;  and  the  '  predicate  term '  of  a  predication 
— that  term  by  which  the  describing  is  done — is 
always  either  an  obvious  class-name,  whether  sub- 
stantive, adjective,  or  verb,  or  a  combination  of  such, 
or  else  is  a  proper  name  turned  into  a  class-name  for 
the  time.  Thus  if  we  describe  Smith  as  a  traitor,  or 
as  treacherous,  or  as  betraying  his  party,  we  are 
evidently  classifying  him  (or  his  actions);  while  if 
we  describe  him  as  '  a  Judas '  we  are  still  chissifying 
him,  l)ut  less  evidently.  In  the  latter  case  we 
probably  mean  that  he  is  a  particularly  treacherous 
kind  of  traitor;  whenever  a  proper  name  is  used 
in    this  manner  it  amounts  to  saying  that    S  (the 

*  The  usual  account  of  tliese  is  discussed  iu  §  54. 


■4 


'% 


4 


'  Subject ')  belongs  to  an  imaginary,  unnamed  sub- 
class within  a  larger  class  roughly  indicated.  A 
further  account  of  the  latter  mode  of  description  will 
be  more  in  place  in  §  37. 

These  verbally  simple  instances  of  the  act  of 
description  must  not,  however,  be  allowed  to  occupy 
our  attention  exclusively.  If  typical  at  all,  they  are 
typical  rather  of  the  elements  into  which  actual  cases 
of  description  may  be  analysed  than  of  acts  of 
description  generally.  For  in  the  first  place,  de- 
scription— especially  where  accurate  description  is 
attempted — is  more  often  than  not  many-worded ; 
and  then  is  more  naturally  viewed  as  a  group  of 
predicative  statements,  each  modifying  the  other, 
than  as  what  Formal  Logic  naively  calls  a  single 
proposition, — like  '  Smith  is  a  traitor,'  or  '  Socrates 
is  mortal.'  The  distinction  between  'one'  proposi- 
tion and  two  or  more  propositions  taken  together  is 
of  tlie  most  external  and  superficial  kind.^  No  limit 
can,  in  theory,  be  set  to  the  complications  that  are 
possible  within  a  single  assertion.  But  since  in 
<,'omplex  predications  some  parts  are  more  open  to 
criticism  than  others,  it  is  usually  necessary  to  break 
them  up  into  portions — of  quite  irregular  size  how- 
ever— which  can  be  considered  separately.'''  In  this 
way  any  complex  predicate  is  merely  a  bundle  of 
simpler  predicates  each  of  which  is  either  a  class- 
name  or  meaningless. 


*  In  tact,  since  every  ]nedicate  term  is  definable  by  genus  and  differentia 
(or  since  every  1*  =  I)(«),  it  follows  that  *  S  is  P  '  always  contains  the  two  pro- 
jM.sitions  *  S  is  D '  and  '  S  is  0.' 

'^  The  confusion  that  may  result  from  not  doing  so  is  exemplified  in  sucli 
phrases  as  'believing  tlie  Bible'  or  'believing  Darwinism.'  One  might 
as  well  speak  of  ]>elieving  philosophy,  or  believing  the  newspapers.  Criticism 
f^iins  more  by  breaking  u)>  aj>parently  simple  assertions  into  their  component 
parts  than  by  reversing  the  process. 


f 


144 


USE  OF  WORDS  IN  REASONING       part  ii 


And  in  the  second  place,  statements  which  have 
an  obvious  Subject  term,  such  as  Smith  or  Socrates, 
do  not  well  illustrate  the  usual  manner  of  stating — 
i.e.  describing— facts  observed.     Though  description 
of  fact  is  essentially  a  predicative  operation,  it  is 
often  not  easy  or  natural  to  throw  it  into  any  form 
which   distinguishes    Subject   from  Predicate.      Not 
only  in  hurried  statements  like  *  Fire  ! '  or  '  Thieves  1 ' 
or  in  cases  where  {e.g.)  *  It  is  raining')  the  extent 
of  the  Subject  is  too  vague  to  be  specified,  but  also 
in  a  very  large  number  of  the  most  ordinary  state- 
ments of  fact  the  Subject  term,  as  such,  either  needs 
no  expression  or  for  some  reason  finds  none.     A  fact 
observed   is   very  commonly  an  event  —  something 
that  takes  place — a  change  that  occurs  in  circum- 
stances taken  as  approximately  known  ;  and  then  we 
naturally  do  not  name  these  circumstances  as  S,  and 
describe  them  as  having  become  P,  but  we  take  the 
S  for  granted  and  merely  speak  of  the  change  itself. 
We  should  naturally  say  **  There  is  a  shooting  star," 
or   **  It   is   getting   lighter,"    rather   than    use  some 
sentence  in   which  {e.g.)  ''The  sky"   would  be  the 
subject  term.     In  other  statements  again  there  are 
two  things  so  equally  spoken  of  that  the  question 
which  is  Subject  and  which  is  Predicate  is  not  easily 
answered.     If  I  say  that  the  motor  car  is  supplanting 
the  horse,  it  is  not  clear — and  can  at  most  be  guessed 
from  the  context — whether  motor  cars,  or  horses,  or 
both,  are  the  Subject. 

Instead,  then,  of  taking  '  S  is  P '  as  the  type  of 
descriptive  assertion,  w^e  may  regard  it  as  only  one 
among  other  forms  appropriate  for  that  purpose.  To 
call  it  specially  the  '  logical  form '  ^  means  no  more 

1  See  chap.  x. 


CH.  V,  .^31      DESCRIPTION,  IN  GENERAL 


145 


s 


than  that  it  is  the  form  on  which  the  machinery 
of  the  Aristotelian  Syllogism  is  based ;  and  that 
machinery  has  perhaps  retained  and  cheapened  the 
name  of  Logic  too  long.  About  the  process  of 
description  the  truth  which  has  special  logical  im- 
portance is  that  we  cannot  describe  anything  without 
using  class-names  (or  other  names  temporarily  made 
into  class-names)  by  which  to  perform  the  operation. 
In  order  to  be  descriptive  at  all  a  name  must  have 
all  the  qualities  and  defects  of  a  class-name,  and  we 
shall  presently  inquire  more  closely  what  these  are. 

$j  31. — All  Statement  of  Fact  is  Description 

But  first  there  is  a  point  which  needs  a  little  dis- 
cussion,— the  question  how  far,  or  in  what  sense,  it  is 
true  that  all  statement  of  fact  is  description.    Common 
sense  is  inclined  not  to  admit  any  such  thing,  but 
rather  to  assume  that  the  descriptive  statement  of  a 
fact  is  somehow  different  from  its  bare  statement,  the 
former  be  in  Lj;  partly  imaginative  like  a  painted  portrait, 
while  the  latter  is  plain  and  straightforward  like  a 
photoujraph.     This  is  one  of  the  many  cases  where  an 
abstract  distinction  wdth  a  certain  rough  value  works 
mischief  when  we  forget  its  abstractness  and  so  trust 
its  applications  unguardedly.     The  unsatisfactoriness 
of  the  assumption  that  any  fact,  as  known  to  us,  is 
i»are  fact,  has  been  already  briefly  noticed  above,^  but 
it  may  be  seen  still  more  clearly  if  we  try  to  imagine 
any  apprehension  of  a  fact  which  does  not  also  involve 
conception  of  it  as  having  such-and-such  characters, 
or  to  imagine  any  real  difference  between  conceiving 
facts  and  interpreting  facts  by  means  of  theory.     No 

1  Page  93,  and  §  27. 
lO 


i 


146  USE  OF  WORDS  IN  REASONING        partii 

doubt  a  use  may  be  found  for  this  distinction,— as  is 
shown  by  its  wide  acceptance.  Vague  though  the 
distinction  may  be,  its  very  existence  shows  that  it 
has  some  value.  No  doubt  we  should  naturally  talk 
of  interpreting  facts  when  the  facts  themselves  are 
taken  as  certain,  and  of  conceiving  them  when 
they  are  the  kind  of  facts  that  can  evidently  them- 
selves be  misunderstood.  For  instance,  if  we  see  a 
man  running,  and  we  try  to  account  for  the  fact  by 
supposing  that  he  has  just  committed  a  theft,  or  that 
he  wants  to  catch  a  train,  that  would  be  an  attempt 
at  interpretation  ;  while  if  we  see  a  dim  object  in  the 
dusk,  and  are  uncertain  what  it  is,  our  etlbrts  to 
account  for  it  would  be  called  an  attempt  to  conceive 
the  fact.  The  vaguer  the  fact  itself  appears  the  less 
easily  can  we  talk  of  its  *  interpretation.' 

But  this  only  changes  the  form  of  the  ditiiculty, 
by  raising  the  question  which  facts  are  really  certain. 
If  a  complete  answer  to  this  question  could  be  found, 
there  would  be  no  further  use  for  Logic,  or  indeed 
for  any  kind  of  science.  It  is  just  because  all  our 
supposed  facts  contain  a  mixture  of  more  and  less 
deniable  elements  that  any  mistakes  are  made.  And 
it  is  of  course  because  mistakes  are  possible  that 
science  has  a  value. 

The  possibility  of  error  existing  in  the  supposed 
facts  themselves  is  w4iat  shows  that  the  so-called 
conception  of  fact  is  only  a  case  of  quicker  and  less 
conscious  interpretation.  The  facts  themselves  cannot 
be  untrue ;  the  only  thing  that  can  be  untrue  is  the 
account  we  give  of  them,— whether  we  call  it  concep- 
tion or  not.  Suppose  the  case  of  a  man  frightened  by 
having  a  revolver  pointed  at  him ;  he  rapidly  forms 
the  judgment    *  Danger,'  in   consequence   of  a   fact 


CH.  v,  §  31       DESCRIPTION,  IN  GENERAL  147 

which  (you  may  say)  he  first  conceives  and  then  in- 
terprets.    But  the  conception  itself  is  an  interpreta- 
tion, and,  if  for  instance  the  revolver  happens  to  be 
unloaded,  a  wrong  one.     There  is  somethiyig  true  in 
the  fact,  for  we  have  supposed  that  the  object  really 
is  a  revolver  ;  but  there  is  also  something  false  in  it,— 
namely  the  theory  which  makes  the  fact  what  it  is 
for  the  frightened  man.     And  however  extreme  we 
make  the  instance  the  same  result  will  be  found.     I 
have  heard  of  a  railway  passenger  who  went  so  far  as 
to  pull  the  alarm-signal  and  stop  the  train  because  a 
harmless  fellow-traveller  took  a  bicycle-pump  from  his 
pocket  and  looked  as  if  he  might  be  going  to  point  it 
at  her.     Some  of  her  fact  was  correct  enouo-li ;  the 
object  really  was  a  sliiny  metallic  cyhnder  with  a  sort 
of  resemblance  to  a  pistol  barrel.     But  so  far  as  the 
fact  was  false  the  error  arose  through  misconception 
or  misinterpretation,  whichever  we  choose  to  call  it. 
Similarly  all  recognition  of  fact  as  such-and-such  a 
kind  of  fact  involves  interpretation  of  a  part  of  it, 
which  is  also  itself  a  fact  recognised    and  therefore 
itself  compounded  of  fact  and  theory;  so  that  w^e 
never  really  get  down  to  the'  bare  fact  on  which  the 
structure  of  theory  is  built.     We  call  a  fact  bare  only 
when  we  have  stripped  from  it  that  part  which  seems 
to  ourselves  to  be  theoretical.     The  only  kind  of  con- 
ception of  fact  known  to  us,  or  imaginable  as  existing, 
is  that  whicli  builds  a  structure  of  more   deniable 
theory  upon  a  basis  of  something  less  easily  denied. 

The  student  would  find  it  a  useful  exercise  to  try 
to  imagine  any  cases  of  false  observation  which  are 
not  cases  of  false  theory,  false  conception  of  the  nature 
of  the  fact  observed.  In  what  direction  is  he  to  look 
for  them  ?   Certainly  you  can  find  true  facts, — or  what 


148  Ut^E  OF  WORDS  IN  llEASONING       part  ii 

pass  for  such  with  all  of  us -facts  in  which  the  theo- 
retical element,   though   it  exists,  escapes  our   own 
recoc^nition  ;  but  the  moment  you  imagine  an  observed 
fact'to  be  false  you  cannot  help  imagining  it  as  a  true 
fact  falsely  conceived  or  interpreted.     If  our  descrip- 
tion  of  a  piece  of  fact  is  inaccurate  the  inaccuracy  can 
only  consist  in  u  talse  theorisation  of  that  fixct,  a  false 
estimate  of  the  nature  and  relative  importance  of  the 
details  composing  it.     That  there  /.  a  fact,  composed 
of  details,  is  always  true ;  untruth  only  begins  with 
our  account  of  what  those  details  are  and  what  notice 
they    respectively    deserve.     In   denying    a  fact   we 
never  deny  that  somethinij  is  true ;  we  only  deny  the 
accuracy  of  the  account  that  is  given  of  that  some- 
thincT  ;  certain  detail,  .uo  overlooked  or  are  given  too 
much  importance.     It  is   in  this  way,  then,  that  all 
statements  of  fact  are  descriptive.     Whenever  a  fact 
is  stated  at  all,  but  more  especially  *  when  it  is  pro- 
duced  as  evidence  for  a  conclusion  and  so  is  taken  as 
havincr  particular    consequences,    its    truth    may    be 
examined  on  exactly  the  same  lines  as  that  of  the 
simplest  possible  predication  about  a  Subject. 

I    Althoucrh    Strictly  speaking,  all  .h-scrii.tiou  or  coucei^tioii  is  for  the  sake 
of  j:^:Xl'^o^^^  looser  expression  without  any  harn. 


CHAPTER    VI 

THE    NATURE    OF   CLASSES 

j:f  :32.— Meaning  of  the  Word  'Class' 

If  it  be  asked  w^hy  it  is  important  to  recognise  that 
description  can  only  be  performed  by  means  of  class- 
names,  or  other  names  used  as  class-names,  the  answer 
is  that  in  the  light  of  this  recognition  we  can  best 
understand  the  defects  to  which  all  description — and 
therefore  all  statement  of  fact — is  liable ;  the  faults 
whi(jh  remain  to  cause  (confusion  and  error  even  where 
the  faulty  description  seems  most  accurate.  But  the 
clearness  of  our  view  of  tliese  defects  greatly  depends 
ui)on  our  view  of  the  nature  of  classes,  and  there  are 
few  sul)jects  about  which  the  liabits  of  common-sense 
thought — encouraged  l)y  Formal  Logic — are  more  con- 
fused and  self-contradictory.  For  reasons  which  will 
be  discussed  in  the  next  chapter,  our  natural  tendency 
is  to  overlook  or  forget  the  fact  that  class-names 
inevital)ly  liave  a  quality  in  them  which  is  the 
parent  of  ambiguity ;  and  the  result  is  that  only  the 
coarser  and  less  effective  kinds  of  ambiguity  obtain 
recognition. 

The  word  '  class '  is  so  commonly  used  that  it  can 
Iiardly  Ije  thought  to  require  translation.  Still,  it  is 
often  taken  in  too  restricted  a  sense.     Social  divisions, 


150 


USE  OF  WORDS  IN  REASONING       tart  ii 


even  vague  ones  like  that  between  rich  and  poor,  are 
of  course  always  recognised  as  class-divisions  ;  so  are 
those  between  classes  in  natural  history,  like  '  verte- 
brates,' '  mammals,'  and  hundreds  more  ;  but  many 
(croups  of  persons  or  things  are  commonly  spoken  of 
by  other  names,  such  as  race,  or  nation,  or  breed,  and 
there  may  be  some  people  who  would  hesitate  to  use 
the  word  *  class '  in  cases  of  this  sort, — to  apply  it, 
for  instance,  to  human  beings  in  general,  or  even  to 
Englishmen  or  negroes.  Still  more  unusual  is  it  to 
speak  of  substances  ^  like  gold  or  wood  or  stone  as 
classes  ;  or  again  of  abstractions  like  deceit,  adversity, 
or  excellence.  These  latter  are  often  conceived  as 
names  of  attributes  ^  rather  than  of  classes. 

The  first  of  the  aliove  three  kinds  of  restriction  on 
the    meaning   of  the   word   '  class '   has    never    been 
adopted  in  Logic,  but  logicians  are  often  under  tempta- 
tion  to  support  the  other  two.     For  our  purposes, 
however,   all    three    may    be   disregarded,   since   the 
truths  which  we  are  here  concerned  with  hold  good 
of  classes  not  only  when  the  word  is  taken  in  one  of 
its  narrower  meanings  but  also  when  it  is  applied  to 
any  group  w^ith  special  characteristics,  whether  {e.(j.)  a 
race  of  men,  or  a  substance  divisible  into  parts,  or  an 
attribute  which  occurs  in  different  individual  cases. 
By  a  class  will  here  be  meant  any  imagined  group  of 
individual    cases,    whether   material    things    or    im- 
material, whether  real  or  unreal,— a  group  in  which 
every    individual    is   supposed   to   resemble    all    the 
others  in   some  respects  though  differing  in  others. 
There    are    classes    of   actions    and  events,  just  as 
of  anything    else  ;    '  miracle '  is  a  class  -  name,    for 
instance  ;    or    '  coronation,'     '  battle,'    *  eclipse ' ;    in 

1  See  end  of  ^  54.  -  See  S  56. 


rn.vi,.^33       THE  NATURE  OF  CLASSES 


151 


I 


fact,  any  name  which  is  used  so  as  to  admit  of  a 
plural,  —  either  simply,  as  '  miracles,'  *  negroes,' 
'  battles,'  or  in  the  more  circuitous  form  of  '  pieces 
of  gold,'  '  cases  of  deceit,'  and  so  on.  If  a  word  which 
was,  or  is,  a  proper  name— say  Hooligan,  or  Jingo — 
acquires  a  plural  form,  that  is  grammatical  evidence 
of  its  having  become,  in  certain  uses,  a  class-name. 
By  English  grammar,  adjectives  in  a  plural  form, 
such  as  *  radicals,'  or  '  imbeciles,'  are  generally  con- 
sidered to  have  become  (in  that  usage)  substantives ; 
but  adjectives,  as  such,  are  class-names,  even  when 
we  have  to  supply  a  word  like  '  persons '  or  *  things ' 
to  make  them  plural.  Verbs  too  are  class-names ; 
for  a  verb  may  at  any  time  be  used  as  a  predicate, 
and  when  so  used  it  is  always  translatable  into  the 
'  logical  foi-m '  which  separates  the  predicate  itself 
from  the  mere  sign  of  predication  ;  ^  and  the  predicate 
thus  separated  is  plainly  either  adjectival  or  substan- 
tival, whichever  we  choose  to  call  it. 

5^  33. — Ancient  and  Modern  View  of  Classes 

A  comprehensive  short  account  of  the  defect  of  the 
popular  view  about  classes  is  that  it  conceives  them 
too  rigidly,  recognises  too  little  that  the  grouping  is 
imaginary,  changing  with  the  changing  purposes  for 
which  it  is  wanted.  But  since  this  false  conception 
shows  itself  in  various  special  ways  we  shall  learn 
more  about  it  by  considering  some  of  these  separately. 
Among  them  may  be  noticed,  for  example,  a  dis- 
inclination to  recognise  any  artificial  element  in 
'  natural '  classes,  or  to  admit  the  continuity  of 
Nature,  or  to  admit   that  all  classes  are  indefinite. 

1  See  §  58. 


1? 


152 


USE  OF  WORDS  IN  REASONING       partii 


Or  again,  indefiniteiiess  and  ambiguity  are  commonly 
taken  for  the  same  thing,  and  vvliile  some  words  are 
recognised  as  suffering  from  this  defect,  it  is  supposed 
that  others  are  entirely  free  from  it ;  and — among  the 
latter  kind  of  words  at  least— the  '  correct  meaning' 
of  a  name  is  a  common  object  of  search,  and  once 
found  it  is  held  to  constitute  an  impassable  barrier 
for  thought.  For  example,  if  the  class  '  man '  in- 
cludes in  its  general  definition  some  particular  attri- 
bute X,  then  it  is  supposed  that  the  question  whether 
men  ever  existed  without  X  cannot  even  be  asked, 
since  it  involves  a  contradiction  in  terms. 

The  exami)le  just  quoted  is  perhaps  rather  extreme, 
for  the  present  day  at  least.  And  indeed  to  find 
these  views  flourishing  (^uite  freely  we  must  go  back 
to  the  Logic  of  the  early  Middle  Ages  when  the 
Realists  were  the  dominatit  school  of  thought, — when, 
for  example,  it  was  assumed  to  l)e  an  easy  matter  to 
say  which  attributes  of  a  class  really  l)elonged  to  its 
*  essence,'  and  which  were  only  '  properties,'  and 
which  were  *  accidents.'  For  in  those  days  man  had 
hardly  begun  to  be  aware  of  the  extent  of  his  own 
itmorance  of  the  facts  and  the  laws  of  Nature,  and 
accordingly  the  real  difficulties  of  definition  were 
kept  in  the  background  without  any  effort.  Natural 
classes,  it  was  then  habitually  supposed,  had  no 
dependence  upon  man's  way  of  regarding  facts.  The 
received  idea  was  that  natural  classes  were  simply 
made  for  man,  and  made  w4th  clear-cut  edges ;  and 
that  man  had  nothing  to  do  but  to  accept  them  and 
learn  their  names  and  their  definitions.  Doubts  as 
to  the  application  of  a  class-name  were  supposed  to 
be  the  fault  or  misfortune  of  the  doul)ter,  not  of  the 
name.      And  even  when   it  was   admitted   that  the 


CH.  VI,  ij  34       THE  NATURE  OF  CLASSES  153 

original  invention  of  the  names  was  of  human  oriorin, 
still  the  process  was  conceived  as  scarcely  more  than 
that  of  finding  suitable  labels  for  things  *  brought  to 
us '  ready  sorted,  like  the  beasts  in  the  Garden  of 
Eden.  It  is  not  easy  for  a  modern  man,  however 
unphilosophical,  to  put  himself  completely  back  at 
this  point  of  view,  but  he  may  come  nearest  to  it  by 
observing  the  ease  with  which  a  child  will  accept 
merely  verbal  explanations.^  The  more  childish  we 
are,  as  individuals  or  as  a  race,  the  more  content  we 
are  to  accept  classes  and  class-names  as  given  facts 
without  further  inquiry. 

But  the  half-truths  of  the  present  day  are  what  we 
are  here  specially  concerned  w^ith,  and  the  older  forms 
of  them  are  of  interest  only  so  far  as  they  help  us  to 
see  more  clearly  the  gradual  change  of  view  that  is 
still  taking  place,  and  to  explain  the  less  careful 
existing  views  as  survivals.  That,  however,  is  by  no 
means  their  whole  explanation,  and  does  not  quite 
account  for  their  vitality.  Under  all  their  various 
forms  we  may  also  see  a  better  excuse  for  them  than 
either  mere  ignorance  or  a  disinclination  for  original 
thought.  For  they  are  all  directed  against  verbal 
quibbling,  and  their  good  intention  fails  chieffy  because 
of  a  certain  lack  of  discrimination  which  leads  them 
to  carry  on  the  war  clumsily  and  with  an  excess  of  zeal. 

S  34. — False  Interpretations  of  the  Modern 

View 

For  instance,  when  the   artificiality  of  classes  is 
spoken  of,  common  sense    remembers  that  artificial 

'  This  is  fjuite  ajiart  from  the  habit  some  children  acMjuire  of  aimlessly 
playing  the  game  of  asking  'Why,'— e.g.  "  Why  is  Grannie  old?"  The 
latter  kind  of  questions  seem  to  have  little  to  do  with  the  search  for  know- 
ledge. 


154 


USE  OF  WORDS  IN  REASONING       part  ii 


11 


and  natural  are  sharply  opposed  ideas,  and  remembers 
also  that  the  distinction  is  actually  in  use  for  the 
purpose  of  marking  off  two  contrasted  types  of 
classification.  It  is  only,  of  course,  the  doctrine 
that  all  classes  are  artificial  that  common  sense 
rebels  against.  That  some  classes  are  so  every  one 
would  allow,  for  we  know  all  about  the  way  they 
were  made, — the  class  '  peers '  for  example,  or  any 
classes  that  depend  upon  distinctions  which  are 
evidently  an  aff*air  of  human  convenience  from  be- 
ginning to  end ;  such  as  our  classes  of  weights  and 
measures,  or  the  distinctions  between  coins  of  different 
value,  or  between  kinds  of  railway  carriages.  In  all 
such  cases  it  is  easy  to  see  that  a  slight  difference  of 
purpose  might  alter  the  classification  considerably, — 
we  may  adopt  the  metrical  system,  or  a  decimal 
coinage,  or  abolish  second-class  carriages.  But  the 
plain  man  distrusts  and  dislikes  the  idea  that  natural 
classes  can  be  in  any  sense  artificial ;  he  suspects  a 
sophistry  on  the  part  of  those  who  tell  him  so,  and 
imagines  they  are  going  on  to  prove  in  over- 
ingenious  ways  that  everything  is  something  other 
than  it  is,  and  to  pretend  that  vulgar  superstition  is 
the  sole  explanation  of  the  widespread  belief  to  the 
contrary. 

And  no  doubt  there  is  some  excuse  for  this 
suspicion,  quite  apart  from  any  desire  on  the  part  of 
common  sense  to  find  philosophy  absurd.  If  we  look 
at  the  phrases  in  which  the  modern  view  of  classes 
has  from  time  to  time  found  expression  we  may 
readily  admit  that  they  are  not  quite  satisfactory. 
But  that  is  everywhere  the  way  with  concise  ex- 
pressions,— as  a  rule  they  lie  open  to  caricature  and 
misrepresentation.     It  would  be  better  therefore  to 


cn.  vr,5^34       THE  NATURE  OF  CLASSES 


155 


use  these  short  phrases  as  little  as  possible,  at  least 
until  w^e  recognise  clearly  that  the  sense  in  which 
they  are  to  be  taken  is  one  that  need  not  cause 
offence  or  impatience. 

For  example,   to  call  classes  artificial   does  not 
mean  that  there  is  nothing  natural  in  them,  or  even 
that  they  lack   reality  or  importance.     We  are  not 
asked  to  suppose  that  class-names  are  invented  for 
mere  amusement  or  for  want  of  something  better  to 
do.     Nor  are  we  called  upon  to  condemn  as  useless 
lor  all  purposes  the  convenient  loose  distinction  that 
is  commonly  made,   under  the  terms  artificial  and 
natural,  between  classes  which  are  arbitrarily  formed 
and  those  which  are  not  so.     There  are  evidently 
some — the  class  '  gold,'  for  instance,  or  any  of  the 
other  supposed  chemical  elements — which  seem  forced 
upon  us  as  objective  facts.     So  far  from  there  being 
anything  arbitrary   in   forming  the   class   gold   and 
drawing  a  firm  line  between  gold  and  other  metals,  it 
has  been  the  desire  of  man  for  centuries  to  break 
down  this  line  of  division,  and  he  has  never  yet  been 
able  to  do  so.     That  there  are  in  this  sense  natural 
classes  no  one  can  dream  of  denying.     To  say  that  all 
classes  are  artificial  must  therefore  not  be  taken  to  con- 
flict with  the  admission  that  some  classes  are,  for  all 
practical  purposes  to-day,  conspicuously  definite  and 
unlikely  to  need  any  change  of  definition  to-morrow. 
Natural  classes,   as  opposed   to    artificial    ones,    can 
only    mean    those   the   precise   limits   (the   dividing 
lines)  of  which  are  so  clearly  marked  that  as  Mill  ^ 
says,  *'  it  is  not  optional  but  imperative  "  to  recognise 
them  ;  or  in  other  words,  that  difficulties  of  definition 
cannot  arise.     And  when  we  ask  which  in  fact  these 

*  Logir^  book  i.  chap.  vii.  §  4. 


H 


156 


USE  OF  WORDS  IX  REASON ISG       part  ii 


CH.  VI,  §  34       THE  NATURE  OF  CLASSES 


157 


classes  are   it  is  evident  in  the  first  place  that  our 
answer  must  depend  a  good  deal  on  the  standard  of 
clearness  of  division  we  happen  to  be  using.     There 
is  no  one  standard  of  clear  division,  as  opposed  to 
rough   division,   which   can    he   used  on   all   possible 
occasions,  unless  indeed  we  decide  to  call  only  those 
classes  *  natural '  in  which   the  drawing  of  the  line 
is  a  matter  mtirety  outside   human   control.     And 
then  we  should  be  raising  a  question — the  question 
which   these  *  imperative*  classes  are  —  that  cannot 
be  answered   until   that  inhnitely  distant  day  wlicn 
we  shall  know  for  certain  that  the  progress  of  know- 
\ed^e  has  come  to  an  end.     Moreover,  so  far  as  the 
ditference   between   good  and   bad   reasonin<]j  is  con- 
cerned  there  is  nothing  gained  by  asking  liow  many 
of  these    fortunate    words   a   rigorous   search    won  hi 
discover,  nor  need  we  dwell  on    tlie  ditKculty  there 
w^ould   be  in   draw  ing   up   any  list  of  them  so  as  to 
satisfy  at  the  same  time  those  who  know  nmcli  ami 
those  who  know  little  about  the  things  to  which  the 
names  belong.     Suffice  it  to  notice  that  if  any  name 
were  really  safe  against  future  changes  of  definition 
then    it  could   not  give  rise  to   those    occasions   of 
difficulty  which  are  of  special  interest  to  the  theory 
of  Logic   as  contrasted  with  common  sense.     From 
the  point  of  view,  therefore,  which  is  taken   in  the 
present    inquiry,  such   names   (supposing   they  exist 
at  all)  would  ])e  the  least  interesting  or   important 
class  -  names   of  any.       Sinc-e   their    application    as 
predicates  is  never  doubtful  they  cannot   illustrate 
effective  errors  of  description.     In  order  to  do  that, 
we  must  consider  the  normal  class-name,   which  is 
always  a  highly  artificial  instrument. 

Nor   again   must  we  suppose  that  to  call  a  dis- 


tinction artificial  is  to  condemn  it  outrio^ht.^  Even 
though  artifice  involves  pretence,  it  is  a  kind  of 
pretence  that  may  be  of  the  utmost  value, — the  kind 
of  pretence  that  has  a  legitimate  purpose  and  is  not 
afraid  of  investigation ;  the  kind  of  pretence  indeed 
without  which  thought  could  scarcely  exist.  To 
recognise  that  predicate  terms  depend  on  artificial 
distinction  is  certainly  to  recognise  that  their  applica- 
tion in  any  given  case  is  disputable ;  but  to  call  an 
assertion  disputable  does  not  mean  that  it  must  be 
untrue,  or  even  that  we  are  bound  to  dispute  it  in 
season  and  out  of  season  ;  it  only  means  that  when  a 
doubt  has  arisen  whether  S  is  P  or  only  seems  to  be 
so,  we  are  at  liberty  to  recognise  that  S  can  only  be 
called  P  for  reasons  of  some  kind,  and  that  such 
reasons  may  perhaps  not  bear  close  investigation. 

Similarly  the  doctrine  that  Nature  is  continuous 
throughout  nmst  not  be  taken  in  any  of  its  obviously 
foolisli  senses.  Some  people  seem  to  fancy  that  what 
is  denied  is  the  existence  of  differences  in  Nature. 
There  could  not  be  a  greater  mistake ;  nothing  of  the 
M>rt  can  ever  have  been  seriously  intended.  Rather, 
we  start  with  the  free  admission  that  Nature  abounds 
in  differences,  and  indeed  that  there  is  no  *  distinction 
without  difference '  except  in  the  sense  that  some 
differences  are,  for  a  given  purpose,  unimportant,  and 
may  thus  become  negligible  on  occasion.  Even 
wliere  the  line  between  two  classes  is  at  its  haziest  the 
difference  betw^een  two  classes  is  a  real  fact  in  Nature  ; 
what  is  not  real  but  artificial,  in  these  cases,  is  the 
sharpness  of  the  distinction.  For  instance,  wealth  is 
a  different  thing  from  poverty,  however  gradually  the 
chan^je  occurs  in  a  ^iven  case. 

*  See  also  }».  101. 


II 


i| 


N 


158 


USE  OF  WORDS  IN  REASONING       part  ii 


Nor  again  is  this  view  bound  up  with  any  particuhir 
theory  of  the  course  of  evolution  in  Nature  ;  we  may 
admit  for  instance  that  between  living  and  not-living 
matter  none  but  an  artificial  line  can  be  drawn,  and 
yet  confess  our  ignorance  of  the  earliest  origin  of  life  ;  * 
it  is  enough  to  recognise  that  dead  food  every  day 
becomes  the  living  body.  The  general  question  as  to 
the  oyWiw  of  life  lies  entirely  aside  from  the  admission 
here  required,  although  no  doubt  the  recognition  that 
classes  are  artificial  paves  the  way  for  many  such 
special  inquiries  into  the  course  of  Nature, — inquiries 
which  could  otherwise  never  be  begun. 

And  the  doctrine  that  class-names  have  no  *  correct ' 
meaning  needs  even  more  care  in  interpretation.  The 
mental  attitude  against  which  it  is  directed  cannot  be 
entirely  condemned,  since  it  depends  upon  qualities 
useful  at  least  in  childhood ;  and  its  chief  defect  is 
that  like  other  useful  early  habits  it  so  often  survives 
its  uses  and  clogs  the  mind  of  the  man.  Therefore 
when  we  protest  against  the  assumption  that  words 
have  a  correct  meaning  it  is  never  intended  to  deny 
that  there  are  words  whose  meaning  remains  almost 
constant,  and  about  which  most  people  are  usually 
ac^reed ;  nor  to  deny  that  some  definitions  of  a  word 
are  better — more  useful  or  less  misleading — than 
others.  We  may  fully  admit  that  dictionaries  and 
textbooks  give  valuable  infonnation  of  a  kind,  and 
that  the  inquiry  after  the  accepted  sense  of  a  word  is 
a  legitimate  inquiry  and  in  some  ways  important ; 
we  may  fully  admit  also  that  the  world  is  on  the 
whole  wiser  than  the  individual,  and  that  therefore 
the  accepted  sense  of  a  word  carries  a  presumption  in 

*  Or  even,  with  Prof.  Ward  {Xaturalism  and  Agnosticism,  vol.  i.  \\  261), 
of  whether  it  ever  did  originate. 


CH.  VI,  §  35       THE  NATURE  OF  CLASSES  159 

its  favour.     In  fact,  when  we  say  that  there  is  no 
such   thing   as   the   *  correct'    meaning,  all  that  we 
need  really  intend  is  that  the  meaning  of  a  name, 
however  widely  accepted  by  the  best  authorities,  is  an 
unsatisfactory  source  from  which   to  learn  the  facts 
about  any  particular  case  in  which  the  name  is  applied. 
For  inexact  purposes,  or  for  some  elementary  educa- 
tional purposes,  it  may  be  a  help ;  but  it  is  certainly 
also  a  hindrance  to  the  progress  of  knowledge,  and  if 
it  were  taken  seriously  and  used  with  thorough  con- 
sistency it   would   be   an    absolute  bar   to  progress. 
When  any  peculiarity  in  the  usage  of  a  word  is  a  help 
in  expressing  or  seeing  a  truth,  it  is  not  the  logician 
but  rather  the  schoolmaster  who  should  raise  objections. 

§35. — The  'Laws  of  Thought' 

The  point  just  spoken  of  will  best  be  understood 
by  reference  to  the  traditional  axioms  which  are  known 
as  the  Laws  of  Identity,  of  Contradiction,  and  of 
Excluded  Middle— principles  which  still  occupy  a 
prominent  position  in  logical  textbooks,  and  are 
supposed  almost  to  explain  themselves  at  sight  and 
to  serve  as  a  solid  foundation  for  Logic  generally. 

The  first  of  them  is  usually  expressed  as  *  A  is  A,' 

for  example.  Black  is  Black,  or  White  is  White.  There 
could  hardly  be  a  more  respectable  axiom  at  first 
sight.  We  have  here  a  proposition  of  the  familiar 
form  S  is  P,  with  the  difference  that  its  Subject  term 
and  its  Predicate  term  are  the  same.  But,  just  as  in 
the  case  of  Jevons'  principle  of  the  Substitution  of 
Similars,  there  are  two  direct  ways  in  which  such  a 
sentence  may  be  interpreted  ; '  and  one  of  them  makes 

^  Of  indirect  ways  there  may  be  an  infinite  variety.     In  some  of  the  best 
modern  treatises  the  old  names  of  these  Laws  are  preserved  for  truths  of  a 


M 


160  USE  OF  WORDS  IN  REASONING       part  ii 

it  an  empty  truism,  a  purely  alKstract  statement  devoid 
of  all  application  or  meaning,  wliile  the  other  makes 
it  an  exceedingly  loose  and  misleading  half-truth. 
Just  as  Jevons'  axiom  speaks  either  of  things  which 
are  really  alike  or  of  things  which  are  taken  to  be 
alike,  so  the  Law  of  Identity  speaks  either  of  things 
which  are  really  A  or  of  things  which  are  taken  as  A. 
liut  what  meaning  is  to  be  found  in  the  statement 
that  things  which  are  really  A  really  are  so?  How 
does  such  a  statement  either  conflict  with  or  confirm 
any  possible  theory  al>out  the  nature  of  a  thing  which 
happens  to  go  by  the  name  of  A  ?  Tn  order  to  be  an 
assertion  at  all,  and  at  the  same  time  not  to  beg  the 
question  it  professes  to  answer,  it  must  speak  of  actual 
cases  called'  A  (i.e.  taken  as  A),  leaving  the  question 
open  whether  they  are  correctly  so  called  or  not. 
Thus  '  So-called  A  is  really  A/  or  '  No  mistakes  are 

much  more  t'laborati-  kin.l.  That  soiiiethiii-  ol  these  .leei»er  truths  may 
have  K'cn  dimly  seen  hy  the  |.hih)soi.hcrs  who  first  put  torwanl  tlie  Uws  is  a 
iK>ssibilitv  whicli  no  one  can  exactly  deny,  an«l  \vhieh  is  in  any  case  chiefly  a 
matter  of  personal  or  historical  iniiH)rtance  ;  for  we  can  admit  the  truths 
without  torturin-  these  Laws  into  expressing  them.  For  instance  there  is  no 
ditUculty  in  acluiitting,  with  IJosanquet  {Logic,  ii.  207).  th.it  -  m  spite  of  or  in 
virtue  of  the  ditferencesexi.resseil  in  a  judgment,  the  ci.ntent  of  judgment  is  a 
real  identity,  that  is  to  say,  has  a  pervading  unity."  Hut  I  venture  to  think 
that  the  students  who  read  the  textbooks  are  not  in  the  hal.it  of  connecting 
any  such  meaning  as  this  with  the  statement  that  A  is  A  ;  and  the  text- 
books crive  him  no  heli)  towards  doing  so.  Again,  why  sh.mld  this  more 
elaborate  meaning  be  expressed  in  any  less  carefully  guarded  form  than  the 
longer   one   just   'luoted  '     It  does  not  need   the   4uestionabU.   supiwt  of 

tradition.  ,    .    .         ,  .  i.     i      i        i 

»  The  f»>rmal  logicians  difficulty  in  adnntting  this  seems  to  f)e  largely 
due  to  the  confusion  between  assertion  and  sentence.  Formal  Logic  holds 
that  a  proposition  may  si)eak  either  of  '  A '  or  of  '  so-called  A,'  but  that  if  it 
speaks  of  the  former  it  does  not  restrict  itself  to  the  latter.  To  the  formal 
logician  accordingly  the  proposition  « A  is  A  '  has  a  diflerent  Subject  from  that 
of  the  proposition  'So-called  A  is  A,'  since  the  words  in  the  sentence  are 
different ;  and  in  consequence  he  overlooks  the  fact  that  the  former  sentence,  if 
not  interpretetl  to  mean  the  same  as  the  latter,  begs  the  (luestion  whether 
the  information  it  pretends  to  give  is  true.  If  in  saying  that  all  S  are  I'  we 
decline  to  bind  ourselves  down  to  any  i>articular  cases  of  S,  we  might  as 
well  siiy  that  when  S  is  P  it  really  is  so.  To  be  completely  consistent  the 
formal  logician  ought  to  deny  that  any  concrete  example  of  A  may  ever  be 
challenged  to  show  its  right  to  the  name. 


CH.  VI,  §  35       THE  XA TURK  OF  CLASSES  1 6 1 

ever  made  in  the  application  of  names,'  is  the  only 
sense  m  which  the  sentence  <A  is  A'  makes  an 
assertion,  and  then  it  is  plainly  false— if  any  false 
account  of  the  nature  of  anything  is  possible. 

I   hope  it  is  clear,  however,  that  this  criticism 
applies  only  to  the  attempt  to  regard  the  axiom  '  A 
18  A  •  as  a  rule  without  exception8,-exceptions  both 
numerous  and  important.     As  a  half-truth  it  may 
have  some  of  the  rough  value  which  a  proverb  or  a 
<opy-book  maxim  has.     Still  that  cannot  give  it  the 
right  to  check  inquiry  into  the  A-ness  of  thincrs  which 
are  taken  as  A.     Only  if  all  our  asserted  facts  were 
certainties  could  the  Law  of  Identity  be  trusted.     But 
to  admit  that  knowledge  is  progressive  is  to  admit 
tliat  existing  knowledge  is  defective,  and  our  asserted 
tacts   therefore   always  open   to  question.      In  pro- 
portion to  the  defects  of  our  knowledge,  our  '  notions  ' 
— t.e.   the   meanings  which   we   distinguish   by  our 
<lcfimtions-are  abstract  and  wordy.     Here  the  value 
of  the  distinction  between  definitions  and  translations 
comes  again  into  view ;  or  rather  the  value  of  any 
distinction   which   helps   us   to   remember   that  our 
existing  notions  are  more  abstract  than  the  facts  and 
need  constant  revision  in  the  light  of  difficult  cases  — 
eases  not  yet  sufficiently  considered.     Further  progress 
111  knowledge  always  depends  on  our  power  of  seeing 
these  difficulties ;  and  to  preserve  the  power  we  must 
hght  against  the  soporific  influence  of  sham  definitions 
Especially  we  must  guard  against  ever  allowing 
them  to  stand  in  the  way  of  an  inquiry  into  facts. 
I'or  instance,  if  Darwin  had  said  to  himself  that  the 
word  '  species,'  by  its  very  definition,  means  some- 
thing diff-erent  from  '  variety,'  and  that  therefore  it 
must  be  sheer  nonsense  to  talk  of  the  latter  becoming 


r 


\ 


162 


USE  OF  WORDS  IN  REASONING       part  ii 


the  former,  he  would  liave  found  his  inquiry  blocked 
at  the  outset  and  could  not  have  taken  the  steps  he 
actually  took  towards  its  solution.  Some  of  his 
opponents,  using  a  shallow  and  formal  Logic,  have 
even  sought  to  refute  his  conclusions  on  this  very 
ground.^  But  he  saw — what  every  one  now  lias  a 
better  chance  of  seein^j — that  we  cannot  control  the 
facts  of  a  case  by  merely  naming  them.  We  do  not 
raise  and  answer  the  question  how  far  X  and  Y  are 
the  same,  either  by  giving  the  names  a  sharply 
contrasted  meaning  or  by  declaring  them  to  be 
synonymous.  By  doing  either  of  these  things  we  hecj 
the  question, — we  shirk  the  real  labour  of  the  inquiry 
and  pretend  to  have  solved  the  problem  by  the  easy 
method  of  attaching  a  special  meaning  to  a  couple  of 
words.  If  our  knowledge  of  Nature  is  to  grow,  we 
must  be  allowed  the  kind  of  verbal  contradiction 
which,  as  we  saw  in  chap,  i.,  leads  to  a  change  in 
the  definition  of  a  word.  Anytliing  which  —  like 
excessive  respect  for  authority — limits  our  freedom  in 
doubting  whether  '  A '  is  really  A  is  an  influence 
which,  whatever  may  be  said  for  it  on  the  score  of 
discipline  or  the  preservation  of  established  beliefe, 
is  at  any  rate  directly  hostile  to  the  progress  of 
knowledge. 

The  Law  of  Contradiction  is  usually  written  *  A  is 
not  not-A,'  and  in  this  form  it  stands  or  falls  witli  the 
axiom  just  discussed.  Another  form  of  it,  sometimes 
supposed  to  guard  it  against  all  criticism,  is  "  Con- 

*  A  still  feebler  argimieiit,  with  a  similar  defect,  was  used  by  Agassiz  to 
prove  that  s|»ecie3  are  immutable:  "If  species  do  not  exist,"  he  asked, 
•'how  can  they  vary?"  Of  course  the  existence  of  so-called  species  has 
never  been  in  question  ;  the  question  is  as  to  their  nature,  and  this  cannot 
be  solved  by  mere  definition.  We  may  all  grant  that  an  immutable  species 
is  immutable,  but  this  does  not  help  us  to  know  whether  any  such  species 
exists. 


CH.  VI,  §  35       THE  NATURE  OF  CLASSES  1G3 

tradictory  assertions  cannot  both  be  true  at  once."    But 
here  again  two  different  interpretations  are  possible, 
one  making  it  applicable  and  the  other  not.     In  the 
abstract  it  is  of  course  undeniable  that  if  an  assertion 
is  true  its  contradictory  must  be  false,  and  vice-versa  ; 
that  is  an  explanation  of  the  meaning  of  the  word 
*  contradictory.'       But  what  does  this  tell  us  about 
actual  assertions?     Since   the    assertion    is    not   the 
sentence,  but   the  meaning  of  the  sentence,  to  say 
that  we  cannot  at  the  same  time  assent  to  and  deny 
an  assertion  is  no  more  than  to  say  that  our  intended 
meaning  (whatever  it  may  be)  really  is  intended.     On 
the  other  hand,  it   is  not  true  that   of  apparently 
contradictory  sentences  both  at  once  cannot  express 
a  true  assertion  ;  and  this  is  the  only  way  in  which 
the    Law  of  Contradiction  can  be  made  applicable, 
since  examples  of  assertion  take  of  necessity  the  form' 
of  sentences.      Notoriously,   it  often   happens   that, 
(jwing  to  some  ambiguity  in  the  language,  the  appro- 
priate answer  to  a  question  is  '  yes  and  no.'    There  is 
often  a  reasonable    doubt    whether    we  have  inter- 
preted a    given    sentence  correctly,  just  as  there  is 
often  a  reasonable  doubt  whether  the  general  name  A 
is  correctly  applied  in  a  given  particular  case. 

Thirdly,  there  is  the  Law  of  Excluded  JMiddle— '  A 
is  either  B  or  not  B.'  Precisely  the  same  objection 
applies.  If  a  given  term  B  happens  to  be  ambiguous 
these  is  no  trusting  the  axiom  that  it  must  be  either 
affirmed  or  denied  in  this  downright  manner.  When 
the  cross-examining  counsel  demands  from  the 
puzzled  witness  '*  the  plain  answer  Yes  or  No,"  the 
assumption  implied  is  that  ambiguity  is  impossible 
—an  assumption  which  is  easily  made  in  the  interests 
of  falsehood.     And,  apart  from  the  tricks  of  the  law- 


!' 


1G4 


r>/;  OF  WOUnS  L\  HEASOMNG       PAinn 


courts,  wlierever  inquiry  leads  to  the  readjustment 
of  the  meaning  of  any  name — a  process  which  often 
extends  over  a  good  many  years  during  which  the  ohl 
and  the  new  meanings  exist  side  by  side — the  Law 
of  Excluded  Middle,  as  an  applicable  statement,  cannot 
be  trusted. 

These  three  principles,  therefore,  when  taken  as 
the  student  inevitably  takes  them,  pretend  to  justify 
the  practice  of  begging  a  (juestion  by  means  of  a 
name.  Unless  they  are  made  purely  abstract  and 
meaningless  they  all  involve  the  false  assumption 
that  ambiguity  is  impossible.  So  far  as  the  improve- 
ment of  our  existing  knowledge  is  our  object,  the  two 
Laws  that  we  should  keep  ever  before  us  are  these  : 
(1)  Anything  actually  named  A  may  better  deserve 
the  predicate  non-A  ;  and  (2)  No  predicate,  B,  is  so 
safe  against  ambiguity  that  it  may  not  be  asserted 
and  denied  at  once  of  the  same  Subject,  A  ;  such 
assertion  and  denial  being  alike  meaningless  until  the 
ambiguity  is  removed.  For  these  reasons  it  would  be 
difficult  to  find  any  case  where  a  scientific  generalisa- 
tion has  been  improved  except  by  disregarding  the 
traditional  Laws  of  Thought  in  their  only  applicable 
sense. 

§  36. — The  Weak  Point  in  Description 

We  have  now  noticed  a  few  leading  samples  of  the 
kind  of  common  misinterpretation  which  certain  short 
expressions  of  the  modern  doctrine  of  classes  have  occa- 
sionally suffered  from,  but  as  yet  very  little  has  here 
been  said  about  what  it  does  assert  or  how  it  confiicts, 
exactly,  with  the  half-truths  of  common  sense.  The 
latter  question  is  rather  a  large  one,  and  will  be  con- 


CH.  vr,  .^  3G       THE  XATUEE  OF  CLASSES  165 

sidered  in  next  chapter,  l)ut  to  the  former  an  answer 
may  now  be  given  provisionally,  which  can  be  stated 
better,  if  necessary,  when  any  definite  misinterpreta- 
tions of  it  occur. 

Subject,  then,  to  fiiults  which  may  afterwards  be 
found  with  the  statement,  we  can  now  say  that  the 
rhange  from  the  older  to  the  newer  view  of  the  con- 
stitution of  classes  has  been  steadily  in  the  direction 
of  increasing  our  power  of  raising  useful  doubts  or 
(juestions,  of  a  kind  that  were  formerly  in  some 
danger  of  being  thought  impossible.  We  are 
learning  to  expect  that  no  class -attribute  is  to 
be  found  quite  pure  in  concrete  cases,  but  that  in  any 
actual  '  A '  some  non-A  is  entangled.  No  longer 
therefore  does  the  truism  that  A  is  A  forbid  us  to  ask 
whether  in  a  particular  case  the  non-A  element  in  the 
so-called  A  has  received  due  recognition.  We  are 
now  able  to  admit,  not  here  and  there  but  universally, 
that  description — the  application  of  general  names  to 
particular  cases — has  in  it  an  element  of  theory,  and 
so  of  doubtfulness. 

Mucli  of  the  change  of  view  is  due  to  the  greater 
recognition  in  recent  times  of  the  extent  to  which 
difference  pervades  all  things.  So  far  from  denying 
the  existence  of  natural  differences — as  we  saw  above 
that  some  of  our  opponents  mistakenly  imagine — we 
go  out  of  our  way  to  recognise  differences  even  in 
cases  where  they  are  in  some  danger  of  being  over- 
looked. We  begin  by  admitting  not  only  that  one 
class  differs  from  another  but  that  no  class  exists  the 
members  of  which  are  all  exactly  alike  ;  and  that  is 
indeed  the  very  reason  why  class-names  are  needed. 
The  whole  object  of  any  class-name  is  to  group 
together  (for  the  purpose  of  making  general  assertions) 


166 


USE  OF  WORDS  IX  REASONING       partii 


individual  members  which  are  not  only  alike  but 
different ;  and  so  to  give  unity  in  spite  of  difference. 
Just  because  it  gives  this  unity,  a  general  name,  as 
such,  must  fail  to  specify. 

And  so  it  is  that  to  classify  S  as  P  is  always  to 
neglect  as  unimportant  some  real  difference  between 
S  and  the  other  memlicrs  of  that  class ;  and  to  raise 
the  question  whether  S  is  P  is  always  to  ask  whether 
the  difference  neglected  has  not,  after  all,  more  im- 
portance than  the  assertor  supposes  ;  a  question  which, 
as  we  shall  see,  remains  eternally  open  except  for  the 
person  w^ho  (for  reasons  good  or  ]»ad)  has  for  the  time 
decided  to  close  it.  Whenever  the  assertion  is  made 
that  S  is  of  such-and-such  a  kind,  the  meaning  is  not 
that  there  is  an  entire  absence  of  difference  between 
S  and  the  other  members,  but  that  the  difference  is 
(for  some  purpose)  less  important  than  the  resem- 
blance. As  to  the  mere  extent  of  the  difference  or 
resemblance,  our  senses  may  deceive  us ;  as  to  the 
relative  importance  of  the  points  of  difference  or 
resemblance,  that  is  a  matter  of  theory  or  opinion, — 
theory  made  by  fallible  men  with  an  incomplete  ex- 
perience of  the  ways  of  Nature.  It  is  always  an  open 
question,  therefore,  whether  the  class-name  which  we 
apply  to  S  has  not  the  effect  of  exaggerating  the 
importance  of  the  likeness  that  exists.  For  instance, 
it  is  literally  true  that  men  are  animals,  but  to  stop 
at  that  fact, — to  dwell  on  man's  merely  animal  nature 
as  opposed  to  his  difference  from  other  animals — 
w^ould  be  misleading.  Sometimes,  again,  we  hardly 
know  whether  a  generic  description  or  some  narrower 
one  comes  nearer  to  the  truth.  The  man  who  likes 
his  *  kind '  is  not  necessarily  the  man  who  likes  a 
bank-holiday   crowd    at    Margate   or   a   crush    in    a 


CH.  VI,  §  37       THE  NA  TURE  OF  CLASSES  1 6  7 

London  drawing-room.  Always  the  right  of  S  to  a 
place  in  the  class  P  rests  in  the  end  on  a  close  examina- 
tion of  the  extent  and  kind  of  the  resemblances  and 
differences  between  S  and  the  more  clearly  recognised 
members  of  the  class,  coupled  with  an  inquiry  into 
the  reasons  for  constituting  the  class  in  one  way 
rather  than  another.  To  judge  that  S  is  P  is  always 
to  judge  that  S,  in  spite  of  any  difference  from  the 
other  members  of  the  class  P,  yet  resembles  them 
essentially, — ie,  possesses  qualities  which  are  of  the 
essence  of  the  class.  But  the  modern^  meaning  of 
'essence'  differs  from  the  ancient  one  in  being  ap- 
plied to  something  much  more  flexible.  The  essence 
of  a  class,  it  is  now  recognised,  is  not  created  by 
Nature  once  for  all,  but  is  adjusted  and  readjusted  by 
man  to  suit  the  purposes — often  quite  temporary — 
for  which  he  wants  to  group  facts  in  order  to  speak 
of  them.  And  from  this  it  follows  that  whenever 
S  is  classed  as  P  the  question  may  be  relevant  what 
sort  of  a  class  P  is  here  contemplated, — what  is  its 
definition. 


8  37. — Metaphorical  and  Matter-of-Fact 

Description 

Another  concise  account  that  might  be  given  of 
the  difference  between  the  older  and  the  newer  view 
of  class-names  is  that  the  latter  tends  to  break  down 

^  Professor  James  {Prinriplcs  of  Psychology,  ii.  335),  speaking  of  the 
cominon  slavery  to  wonls,  says,  "Locke  undermined  the  fallacy.  But  none 
of  his  successors,  so  far  as  I  know,  liave  radically  escaped  it,  or  seen  that  the 
only  meaning'  of  essence  is  tel('olo*,ncal,  and  that  classification  and  conception 
are  jnirely  teleological  wea|>ons  of  the  mind."  I  cannot  help  thinking  that 
this  newer  view  of  essence  is  taking  pretty  firm  hold  of  us,  and  as  rapidly  as 
could  be  expected.  Is  it  jmssible  for  any  one  to  do  good  original  work  in 
natural  science  without  a  grasp  of  the  doctrine,  that  names  are  artificial  ? 
See  also  my  book  on  J)isfi,ictu>n,  p.  139  and  elsewhere. 


168 


USE  OF  WORDS  IN  REASONING       pakt  ii 


the  loose  convenient  distinction  between  metaphorical 
and  matter-of-fact  description.  We  have  noticed 
already  (p.  142)  that  what  may  he  called  predication 
by  analogy,  or  by  metaphor — e.g.  '  S  is  a  Jvxlas ' — 
only  differs  unimportantly  from  predication  by  means 
of  a  recognised  class-name.  But  we  may  get  a  clearer 
view  of  this  truth,  and  of  the  close  kinship  between 
metaphorical  and  matter-of-fact  description,  through 
seeing  how  the  former  sometimes  l)ecomes  the  latter 
by  imperceptible  degrees.  Words  which  are  obviously 
fanciful  when  first  applied  to  a  given  use  become 
in  process  of  time  accepted  class-names,  and  thus 
instruments  of  the  most  matter-of-fact  description. 
This  is  illustrated  not  only  by  the  occasional  cases 
where  a  proper  name  (like  Merctcry  or  McBander) 
has  become  general,  but  by  every  gradual  extension 
of  meaning  in  an  accepted  general  name.  In  all 
such  cases  the  new  application  seems  at  first  a  little 
strained ;  but  gradually  this  appearance  wears  away, 
and  an  increasing  number  of  people  accept  the  new 
usage  as  plain  description.  Thus  we  speak  now-a- 
days  of  an  investmerit  of  money  in  quite  a  prosaic 
matter-of-fact  way  ;  the  metaphor  by  which  the  word 
came  to  its  present  use  has  entirely  faded  out  of 
notice  ;  we  do  not  habitually  remember  its  connection 
with  vestment.  And  the  same  with  developing  a 
photograph,  or  with  a  word's  derivation. 

There  is  a  difference,  of  course,  between  a  meta- 
phorical or  fanciful  name  and  a  matter-of-fact  one. 
But  the  diff*erence  is  not  so  sharp  and  clear  as  the 
popular  view  assumes.  Description  by  metaphor 
does  not  imply  the  absence  of  reference  to  a  class,  but 
only  the  absence  of  a  clearly  specified  class  referred  to. 
In  every  analogy  or  metaphor  there  is  apparently 


CH.  VI,  §  37       THE  NATURE  OF  CLASSES 


169 


important  likeness  combined  ivith  appay^enthj  unim- 
portant difference,  and  that  is  all  that  there  is  in 
any  class,  however  definite  it  claims  to  be,  and  how- 
ever completely  it  is  recognised  in  a  language.    Again, 
either  kind  of  description  may  be  inaccurate,  in  the 
same  way  and  from  the  same  causes.     The  mistake 
into  w^hich  we  might  fall  when  undue  stress  is  laid  on 
the  distinction,  is  that  there  are  two  kinds  of  descrip- 
tion, one  'matter-of-fact'  and  the  other  analogical, 
metaphorical,  or  fanciful ;  and  that  of  the  two  the 
former  is  clearly  the  more  accurate.    The  better  view, 
when  we  do  not  allow^  the  distinction  to  mislead  us,  is 
that  all  descriptions  are  more  or  less  ftmciful  (or  theo- 
retical), and  that  whatever  advantage  may  be  gained 
by  avoiding   the  more  fanciful  end  of  the  scale  is 
counterbalanced  by  the  false  supposition  that  in  matter- 
of-fact  description  we   are  perfectly  safe.      The  more 
matter-of-fact  a  description  appears  to  be,  the  greater 
pretence  of  accuracy  it  makes ;  that  is  precisely  its 
<langer.     There  is  a  well-recognised  risk  of  caricature 
in  comparing  S  to  marked  characters  in  history  or 
fiction,  but  the  risk  of  caricature  which  lurks  in  all 
predication  is  much  less  well  known,  and  the  error 
is  therefore  less  easily  detected.     And  so,  where  a 
descriptive  name  is  misleading  at  all,  it  is  even  more 
misleading  if  it  happens  to  be  a  recognised  class-name 
than  where  it  makes  less  pretence  of  simplicity,  plain 
statement  of  fact,  or  widespread  acceptance.      The 
class-name  *  gentleman'  may,  for  instance,  be  more 
misleading  in  a  given  case  than  some  metaphorical 
name   like    *a   Coriolanus'    or   *a  Chesterfield.'      A 
class-name  cannot  in  itself  guarantee  its  own  correct- 
ness of  application ;  it  can  add  nothing  to  the  re- 
semblance, nor  diminish  the  difference,  between  the 


170 


USE  OF  WORDS  IN  REASOXIXG       pauth 


cases  covered  l>y  it.  At  most  it  provides  some 
evidence  that  the  world  has  hitherto  imagined  the 
class-resemblance  important  for  a  number  of  ordinary 
purposes. 

A  further  remark  may  also  here  be  in  place.  Sup- 
pose, by  a  stretch  of  imagination,  that  our  insight 
into  Nature,  past,  present,  and  future,  were  somehow 
miraculously  extended  and  deepened,  so  as  to  guard 
us,  in  the  case  of  any  descriptive  term,  against  in- 
accuracy in  its  application,  what  would  be  the  result  ? 
That  term  would  at  once  become  entirely  devoid  of 
descriptive  force.  It  would  become  the  name  of  a 
purely  individual  case, — like  a  proper  name  when  used 
for  mere  reference.  It  would  not  compare  the  Subject 
with  a  class  of  cases  (even  a  class  vaguely  conceived) 
and  declare  that  the  resemblance  is  more  important 
than  the  diiference ;  for,  being  perfectly  definite,  it 
w^ould  not  allow  us  to  neglect  any  existing  difference 
whatever,  and  between  any  two  cases  some  difference 
exists. 

Whether  this  result  seems  paradoxical  or  not,  it 
obtains  some  partial  confirmation  from  the  fact  that 
men  so  often  prefer  loose  and  vague  descriptions,  and 
even  openly  metaphorical  ones,  when  effectiveness 
of  description  is  specially  desired.  Fanciful  names 
are  a  resource  well  known  to  be  useful  where  we  wish 
to  characterise  pithily  some  complex  matter  which 
would  otherwise  need  a  long  roundabout  description. 
The  virtue,  for  instance,  of  a  prominent  person  may 
be  asserted  to  be  *  Pecksniffian,*  or  a  whole  political 
party  picturesquely  described  as  '  rats.'  This  method 
of  characterising  has  easily -seen  advantages  where 
strength  of  assertion  is  desired,  and  it  obviously  saves 
trouble.     No  one,  I  believe,  disputes  the  power  of 


CH.  vr,  §  38       THE  NATURE  OF  CLASSES  171 

these  devices  of  language,  and  at  any  rate  in  the 
more  chastened  forms  in  which  they  occur  in  poetry 
we  feel  that  to  pare  away  their  inexactness  would  not 
be  an  unmixed  gain.  Description  that  comes  near 
caricature  may  even  be  useful  in  setting  our  wits  to 
work  upon  the  task  of  exact  appreciation  of  the 
likeness.  If  the  possibility  of  error  w^ere  banished 
from  the  world,  and  with  it  all  the  indefiniteness  of 
language,  there  w^ould  be  literally  nothing  left  for 
Logic  to  do.  But  this  contingency  is  at  present 
remote  enough  ;  the  names  we  use  are  far  from  being 
always  *  proper.' 

§  38. — Some  Consequences 

One  practical   use  and  application  of  the  newer 
view  of  classes  is  as  against  the  dogmatic  assertor's 
attempt    to    override    inquiry   into    the    truth    of  a 
stated  ffict.     If  there  w^ere  any  predicate  terms  whose 
application  could  never  be  doubtful,  that  w^ould  mean 
that  there  are  predicative   assertions   the    truth  of 
which   lies  wholly   beyond   dispute.      But   no   such 
class  can  be  recognised — except  as  a  mere  abstract 
possibility — by  science  or  philosophy.     We  may  all 
admit  of   course  that  there  are  many  predications 
made  which  it  would  be  the  reverse  of  practical  to 
doubt,  and  which  no  one  but  a  quibbler  w^ould  hesi- 
tate to  accept  as  true.     But  to  accept  a  '  truth '  is 
one  thing  and  to  cut  ourselves  off  from  the  right  of 
questioning  it  at  any  future  time  is  quite  another. 
Often  an  assertion  is  so  unimportant,  or  so  easily 
understood  and  so  little  misleading  in  spite  of  its 
faults  of  expression,  that  there  could  only  be  a  waste 
of  time  in  raising  doubts ;  but  a  doubt  once  actually 


172 


USE  OF  WORDS  IN  REASONING       part  ii 


seeu  demands  attention,  however  unlikely  it  may 
have  seemed  beforehand.  To  call  our  own  assertions 
indisputal)le  is  of  course  always  tempting ;  nothing  is 
commoner  than  the  wish  to  take  up  this  attitude 
towards  our  criti(%s.  But  Logic  does  not  exist  for 
the  sake  of  suppressing  criticism  in  the  interests  of  the 
random  asseitor,  and  though  the  logician  may  (with 
the  rest  of  the  world)  loosely  talk  of  some  assertions 
as  '  indisputable/  he  cannot  (as  the  rest  of  the  w^orld 
contentedly  can)  apply  this  epithet  to  assertions  which 
are  actually  disputed. 

While,  therefore,  it  would  be  foolish  to  suppose 
that  we  can  never  class  a  thing  as  A  without  con- 
sciously and  deli))erately  raising  the  question  w^hether 
it  does  not  rather  deserve  to  be  classed  as  non-A,  it 
must  nevertheless  be  admitted  that  any  name,  pre- 
tending to  be  descriptive,  fails  to  be  so  if  it  declines 
to  face  the  possibility  of  being  wrongly  applied  in 
particular  cases.  In  every  predication  *  S  is  A '  we 
claim  to  have  exercised  a  choice  Ijetween  the  predi- 
cates A  and  non-A,  and  to  have  chosen  the  former 
on  sufficient  grounds.  However  rapidly  and  instinc- 
tively the  choice  may  have  been  made,  the  descrip- 
tiveness  of  either  of  the  opposite  predicates  depends 
on  the  contrast  between  them,  and  the  preference  of 
the  one  to  the  other  when  either  is  applied.  So  that 
a  class  is  not  only  a  grouping  of  individual  cases 
without  regard  to  the  question  what  cases  are  to  be 
excluded,  and  why ;  a  class  is  always  a  sect,  —  a 
portion  cut  out  of  a  larger  w^hole  and  placed  in  imagi- 
nary isolation.  And  this  involves  two  further  conse- 
quences :  (1)  that  a  predicate  term  is  meaningless  if 
it  be  supposed  to  belong  impartially  to  everything  in 
the  Universe  ;  and  (2)  that  in  the  cases  where  a  name, 


CH.  vi,g38       THE  NATURE  OF  CLASSES 


173 


supposed  to  be  descriptive,  is  difficult  to  define  pre- 
cisely, its  descriptive  meaning  rests  on  insecure 
foundations,  and  may  vanish  entirely  on  occasion. 
How  this  total  disappearance  of  meaning  takes  place 
we  shall  inquire  in  the  next  chapter. 

And  apart  from  its  direct  application  against 
wordy  dogmatism,  the  modern  view^  of  classes  has  a 
special  bearing  on  the  question  whether  there  can  be 
such  a  thing  as  a  fact  which  is  *  single,'  or  simple, 
in  anything  but  name.  The  defect,  we  have  seen,  to 
which  class -names  are  liable,  and  which  therefore 
may  affect  any  statement  of  fact,  consists  in  the 
obliteration  of  details  of  difference  w^hich  may  or 
may  not  be  important.  That  they  are  unim- 
portant in  a  given  case  is  always  a  matter  of 
theory,  and  therefore  open  to  question  if  it  should 
seem  worth  while.  But  this  is  to  recognise,  in  other 
language,  that  in  every  statement  of  fact  there  are 
more  and  less  deniable  portions,  or  that  the  fact  as  a 
whole  may  be  split  up  into  fragments,  differing  in 
certainty,  and  that  how^ever  far  we  may  be  led  in 
doing  this  there  is  in  strictness  no  end  to  the  process 
except  where  we  choose  to  make  one.  The  more 
apparently  indisputable  it  is  that  S  is  P,  the  more 
any  actual  dispute  about  that  assertion  must  turn  on 
the  precise  importance  of  the  likeness  and  unlikeness 
of  S  to  the  recognised  members  of  the  class  P.  Thus 
it  is  specially  when  assertions  are  nearly  true  and  yet 
are  disputed  that  we  are  drawn  into  questions  of 
careful  definition.  Downright  errors,  like  the  asser- 
tion that  the  Earth  is  flat,  lie  open  to  condemnation 
by  shorter  and  easier  methods. 


CHAPTER   VII 

indefinitkness  and  ambiguity 

5^  31).— Complete  Descfuption  and  Perfect 

Definiteness 

From  the  admission  that  in  every  chxss  every  member 
differs  to  some  extent  from  every  other,  a  number  of 
other  admissions  follow  which  interfere  considerably 
with  our  acceptance  of  certain  widely-received  half- 
truths  about  the  use  of  words,  and  wliich  thereby 
throw  some  much -needed  light  upon  the  nature  of 
ambiguity,  that  most  effective  of  all  the  avoidable 
sources  of  bad  reasoning.  The  chief  root  of  these 
popular  half-truths  may  be  found  in  the  confusion  of 
ambiguity  with  indefiniteness,  and  the  cliief  result  of 
them  in  the  tendency  to  overlook  the  harm  caused 
by  and)iguity  and  to  minimise  the  importance  of 
detecting  and  removing  it.  In  this  respect  the  main 
difference  between  the  least  scientific  common  sense 
and  the  most  scientific  Logic  lies  in  the  former's 
readiness  to  identify  the  search  for  definitions  with 
unpractical  subtlety  or  mere  quibbling.  Through  its 
confusion  of  indefiniteness  with  aml)iguity  it  loses  the 
power  of  discriminating  between  the  justified  and  the 
unjustified  inquiry  for  definitions. 

In  the  first  place,  then,  if  the  class-name  P,  just 


en.  VII,  §  39  IXDEFIXITEXESS  AXD  AMBIGUITY  175 

l)ecause  it  is  a  class -name,  neglects  the  individual 
differences  between  one  member  of  the  class  and 
another,  the  same  must  l)e  true  of  the  more  restricted 
class-name  AP,  and  of  any  class-name  A  .  .  .  ZP.,  how- 
ever restricted.  In  describing  anything  (S)  as  P,  the 
description  is  evidently  incomplete  in  so  far  as  it 
omits  to  say  what  soi^t  of  P  is  intended ;  and  it 
always  must  omit  this  to  some  extent.  For  instance 
the  description  of  Socrates  as  a  '  man '  evidently 
leaves  room  for  further  characterisation  if  required ; 
but  however  far  the  characterisation  proceeds  we  can 
never  make  it  finally  perfect,  since  it  is  throughout 
performed  l)y  class-names  to  which  the  same  defect 
attaches.  How^ever  many  things  may  be  said  about 
Socrates,  or  about  any  fact  observed,  there  remains 
still  more  that  might  be  said  if  the  need  arose ;  the 
need  is  the  determining  factor.  Hence  the  distinction 
between  complete  and  incomplete  description,  though 
perfectly  sharp  and  clear  in  the  abstract,  can  only 
have  a  meaning — can  only  be  applied  to  actual  cases 
— if  it  be  taken  as  equivalent  to  sufficient  and  in- 
sufficient description,  the  sufficiency  being  relative  to 
some  purpose.  Evidently  the  description  of  Socrates 
as  a  man,  scanty  though  it  is,  may  be  fully  sufficient 
for  the  purpose  of  the  modest  inquiry  whether  he  is 
mortal  or  not ;  and,  generally  speaking,  in  all  descrip- 
tion there  comes  a  point  at  wdiich  even  the  most 
inquiring  mind  is  willing  to  cease,  for  the  time, 
from  collecting  further  details,  and  sets  itself  to 
consider  how  to  use  for  inference  those  already  col- 
lected. 

Secondly,  from  the  admission  that  all  description 
is  necessarily  incomplete,  it  follows  that  every  name, 
however  fully  descriptive,  is  necessarily  indefinite ;  or 


176 


USE  OF  WORDS  IX  llEASOXING       part  ii 


% 


that  the  perfect  and  final  definition  of  any  word  or 
set  of  words  is  impossible.  Passing  over,  for  the 
moment,  our  natural  disinclination  to  admit  this, — 
the  sources  of  w^hicli  will  presently  be  discussed, — it  is 
evident  that  if  it  be  true,  then  the  distinction  between 
perfect  and  imperfect  definition  has  the  same  defect  as 
that  between  complete  and  incomplete  description. 
The  sharpness  of  the  merely  abstract  distinction  does 
not  alter  the  fact  that  if  we  are  to  use  the  distinction 
at  all  w^e  must  translate  *  perfect  and  imperfect '  into 
*  sufficient  and  insufficient,'  again  with  reference  to 
some  purpose  understood.  If  perfect  definition  is 
impossible,  it  is  evident  that  to  ask  intelligently  for  a 
definition  is  not  to  ask  for  a  perfect  one,  and  that  the 
intelligent  complaint  that  a  given  definition  is  im- 
perfect can  only  mean  that  for  some  assignable 
purpose  it  does  not  suffice. 

Now  the  tendency  of  popular  thought — encouraged, 
as  we  shall  see,  by  the  traditional  Logic — is  to  regard 
this  insistence  on  the  diff*erence  between  sufficiently 
perfect  and  absolutely  perfect  definition  as  a  piece  of 
misplaced  ingenuity  or  unpractical  trifling.  No  doubt 
it  would  be  possible  to  use  the  distinction  in  some 
such  spirit,  to  make  perhaps  some  show  of  drawing 
from  it  consequences  destructive  to  all  thinking,  or  at 
least  widely  and  rashly  destructive  to  the  present 
results  of  human  thought  and  experience.  Since  no 
one  can  say  exactly  how  much  earth  added  to  a  mole- 
hill would  convert  it  into  a  mountain,  the  quibbler 
may  seek  to  blur  the  difference  altogether.  But  why 
assume  that  this  is  the  only  kind  of  use  that  can  be 
made  of  the  admission  ?  What  will  here  be  deduced 
from  it  is  an  answer  to  the  problem  what  the  value  of 
any  search  for  a  definiiion  depends  upon,  and  to  the 


CH.  vn,  §39  INDEFINITENESS  AND  AMBIGUITY  177 

further  problem  what  are  the  conditions  of  effective 
and  useful  casuistry. 

The  popular  disinclination  to  admit  that  all  defini- 
tion is  necessarily  imperfect  does  not,  I  think,  generally 
take  the  shape  of  denying  the  statement  itself,  but 
rather  of  denying  its  value  and  of  reckoning  wholly 
without  it — just  as  we  all  reckon  without  the  bare 
possibility  that  an  earthquake  will  destroy  London 
to-morrow.  Still  our  first  step  should  be  to  get  the 
fact  itself  admitted,  irrespective  of  the  question  as 
to  its  importance.  Some  readers  may  fail  to  see  any 
connection  between  the  necessary  incompleteness  of 
all  descripition  and  the  necessary  indefiniteness  of  all 
descriptive  names. 

What  is  meant  is  that  since  the  definition  of  any 
name  P  is  an  attempt  to  describe  the  difference  be- 
tween those  things  which  are  P  and  those  which  are 
not  P  ;  and  since  that  difference,  like  everything  else, 
can  only  be  described  in  general  terms  and  therefore 
incompletely  ;    no    definition    (;an    2^erfectly   define. 
Sufficiently  for  the  purpose  of  a  given   inquiry,  of 
course,  the  feat  is  performed  every  day  ;  but  it  cannot 
be  done  so  as  to  suit  the  purposes  of  every  possible 
inquiry,  future  ones  included.     Or,  to  put  it  in  another 
way,  definition  is  the  attempt  to  decide  what  amount 
and  kind  of  difference  is  allowable  between  members 
of  the  class  P,  or  what  departure  from  the  normal 
type  is  required  to  destroy  a  doubtful  member's  right 
to  the  name ;  and  if  the  answer  is  that  it  does  not 
matter  whether  the  members  are  A  or  not,  but  they 
umst  (or  must  not)  have  the  quality  B,  then — since 
B  is  also  a  general  name — the  same  question  arises  in 
regard  to  membership  in  the  class  B;   and  since  at 
every  step  general  names  are  used  there  is  no  end  to 

12 


178 


USE  OF   WORDS  IN  REASONING       part  ii 


the  inquiry  except  where  we  choose  to  make  one. 
To-day's  needs  may  be  satisfied,  but  to-morrow's 
needs  cannot  be  securely  foretold  and  provided  for. 

§  40. — The  Popular  View  of  Indefinitkness 

AND  Ambiguity 

Let  us  assume,  now,  that  as  a  matter  of  strict 
theory  this  is  admitted.  The  question  remains  what 
use  is  to  be  made  of  the  admission,  and  whether  it 
amounts  to  anything  more  than  one  of  those  theo- 
retical truths  which  are  so  remote  from  practice  that 
the  wise  man  is  he  who  persistently  forgets  them. 
And  to  answer  this  we  must  look  more  closely  at  the 
common-sense  way  of  dealing  with  the  question,  and 
especially  at  the  assumptions  which  underlie  its 
methods.  The  chief  of  these  is,  I  think,  the  assump- 
tion that  indefiniteness  and  ambiguity  are  the  same 
thing,  but  there  are  also  others  so  closely  involved  in 
this  that  in  dealing  with  it  we  can  scarcely  avoid 
meeting  them. 

And  first  as  to  the  facts  of  the  popular  usage. 
Though  loosely-held  views  will  not  bear  stating  as  if 
they  were  consistent  and  precise,  I  think  we  may 
fairly  say  that  to  a  large  number  of  people  it  does 
not  occur  that  indefiniteness  and  ambiguity  are  in 
any  important  sense  different  things.  One  natural 
reason  for  the  confusion  is  that  as  a  rule  we  do 
not  notice  the  indefiniteness  of  a  word  until  it  has 
caused  an  ambiguity,  and  hence  we  tend  to  speak  as 
if  the  two  defects  were  identical.  Since  neither  is 
commonly  *  found '  without  the  other  it  does  not  seem 
to  matter  much  which  name  we  use  for  it  in  a  given 
case.      In  much    the   same  way  crime,  or   heroism, 


CH.  VII,  §  40  INDEFINITENESS  AND  AMBIGUITY  179 

tends  to  be  identified  in  popular  thought  with  only 
the  gross  or  striking  forms  of  it.  Wherever  a  quality 
is  on  some  occasions  difficult  to  detect  there  will  be  a 
tendency  on  the  part  of  the  many  to  identify  that 
quality  with  its  more  obvious  manifestations  only. 
To  a  hasty  or  careless  or  ignorant  view,  the  good  and 
the  bad  are  the  obviously  good  and  the  obviously  bad  ; 
and  to  the  same  sort  of  view  indefiniteness  exists  only 
when  it  has  actually  caused  trouble.  The  most  widely- 
received  opinion  appears  to  be  something  of  this  kind  : 
that  the  indefiniteness  (or  ambiguity)  which  inheres 
in  a  word  is  either  so  slight  as  to  be  of  no  account,  or 
else  so  great  as  to  deserve  the  attention  of  sensible 
men ;  that  theoretical  Logic  may,  if  it  likes,  amuse 
itself  with  the  search  for  an  accurate  definition  in 
either  case,  but  that  only  where  the  indefiniteness  is 
great  can  there  be  any  practical  value  in  the  search. 
It  is  generally  supposed  that  the  latter  case  is  com- 
paratively rare,  but  that  nevertheless  there  are  in 
use  a  certain  number  of  *  highly  ambiguous  words.' 
The  point  of  view  is  similar  to  that  which  is  commonly 
taken  about  unwholesome  food.  The  unwholesome- 
ness  of  any  food,  it  is  said,  is  either  so  slight  as  to  be 
of  no  account,  or  else  so  great  as  to  justify  its  avoid- 
ance by  sensible  men.  Fanciful  people  may  if  they 
like  condemn  this  or  that  ordinary  dish,  but  it  is  only 
when  food  is  *  really  unwholesome '  that  there  is  any 
good  reason  for  avoiding  it.  This  roughly  practical 
way  of  regarding  the  food  question  is  here  quoted  so 
as  to  put  the  case  for  common  sense  fairly.  Whether 
the  analogy  is  complete  or  not  there  can  be  no  harm 
in  assuming,  at  first,  that  the  common  logical  view 
about  ambiguity  is  as  sensible  and  healthy  as  the 
non- valetudinarian  view  about  food.      The  question 


180 


USE  OF  WORDS  IN  REASONING       i-akt  ii 


Is! 


whether  it  is  so  is  the  point  we  have  now  to  discuss. 
Is  the  decree  of  indefiniteness  the  factor  that  de- 
termines  its  importance  ? 

§  41. — Degrees  of  Indefiniteness 

It  is  clear  that  so  long  as  ambiguity  is  identified 
with  indefiniteness  we  cannot  avoid  the  (conclusion 
that  it  is  only  the  degree  of  the  fault  that  matters. 
Since  we  all  instinctively  assume  that  the  same  efiect 
follows  the  same  cause,  the  more  we  are  inclined  to 
identify  ambiguity  with  indefiniteness  the  less  do  we 
naturally  expect  any  difi'erence  between  their  results. 
There  can  be  no  (question,  then,  from  this  point  of 
view,  of  one  being  more  destructive  to  meaning  than 
the  other,  but  the  practical  distinction  (it  seems) 
must  be  between  the  larger  and  effective  kinds  of  the 
defect  and  the  finer  or  scarcely  visible  ones  whic^h 
no  one  but  a  mere  precisian  need  care  to  notice. 

And  this  would  perhaps  do  very  well  if  the  notion 
of  degrees  of  indefiniteness  could  l)e  given  a  (-lear 
and  satisfactory  meaning.  But  the  notions  of  more 
and  less  as  applied  to  indefiniteness  are  difficult  to 
explain,  or  at  least  to  connect  with  the  need  for 
definition,  unless  they  are  made  dependent  on  the 
efiect  produced,  and  then  of  course  it  is  merely 
arguing  in  a  circle  to  make  the  efi'ects  depend  in  turn 
on  the  amounts.  Since  all  descriptive  words,  as 
such,  are  indefinite,  what  can  be  meant  by  calling 
one  more  indefinite  than  another  ? 

Evidently  it  will  not  do  to  make  the  distinction 
turn  on  the  grossness  and  obviousness  of  a  word's 
double  meaning,  for  then  we  should  have  to  admit 
that  the  very  largest  *  ambiguities '   are  those  that. 


CH.vir,Hl   INDEFINITENESS  AND  AMBIGUITY  181 

while  they  may  lend  themselves  easily  to  the  con- 
struction of  puns,  are  certainly  not  effective  sources 
of  error. 

A  show  of  answering  the  question  may  perhaps 
be  made  by  saying  that  words  are  more  and  less 
definite  in  proportion  as  they  have  been  carefully  or 
caielessly  defined,  whether  the  lack  of  definition  be 
due  to  mere  inattention  or  to  the  kind  of  difficulty 
which  attaches,  as  every  one  knows,  to  words  like 
*Life'  or  *  Truth.'  Names  which  either  baffle  defini- 
tion or  whicli  do  not  seem  to  call  for  it  would  then 
be  contrasted  with  names  which  both  call  for  it 
and  get  it, — names,  for  instance,  like  "  £5  Bank  of 
England  Note,"  where  the  required  class-marks  are 
numerous  and  yet  may  be  known  with  great  minute- 
ness. 

But  then  in  the  first  place  the  class  of  *  more 
indefinite'  names  would  include  those  whose  in- 
definiteness is  notorious  and  striking,  and  which  as 
we  have  just  noticed  are  on  that  account  com- 
paratively harmless.  And  in  the  second  place  it 
would  also  include  those  which  all  the  world  rightly 
or  wnmgly  is  content  to  use  with  vagueness  and 
freedom.  Of  course  those  which  are  wrongly  so  used 
are  thereby  shown  to  be  troublesome  words,  but  how 
is  the  same  to  be  said  of  the  equally  indefinite  words 
which  are  rightly  used  without  extreme  precision? 
This  would  be  to  fall  into  the  very  defect — unpractical 
pedantry — which  common  sense  is  so  anxious  to 
avoid.  In  two  ways  therefore  we  fail  to  get  any 
simple  identification  of  the  *  more  indefinite '  words 
with  the  words  which  actually  cause  most  trouble. 
And  on  the  other  hand  it  is  by  no  means  certain 
that  even  the  most  careful  attempts  at  definition  will 


182 


USE  OF  WORDS  IN  REASONING       part  ii 


have  anything  like  the  effect  which  this  view  of  the 
distinction  supposes.  The  leading  technical  terms  of 
Logic  itself  are  an  instance  of  words  which  have 
undergone  plenty  of  careful  definition,  and  what  do 
we  find  as  the  result  ?  *  Indeed,  on  general  grounds 
we  may  see  tw^o  good  reasons  why  it  cannot  be  true 
that  the  most  satisfactory  words  are  those  that  have 
the  most  elaborate  definitions.  For  one  thing,  it  is 
often  the  proved  unsatisfactoriness  of  the  word  which 
has  led  to  the  elaboration  ;  and  for  another  the  very 
fact  that  so  much  care  has  been  taken  is  apt  to 
engender  a  false  security.  Thus  technical  terms  run 
a  special  risk  of  becoming  idols.  The  modest 
beginner  in  Logic  finds  it  hard  to  l)elieve  that  a 
name  like  '  hypothetical  proposition,' "  for  example, 
can  be  used  by  a  logician,  speaking  carefully,  in  such 
a  way  that  neither  the  user  nor  any  one  else  can  say 
which  of  two  different  things  he  has  in  view. 

These  hopeless  attempts  to  make  a  distinction 
between  greater  and  less  vagueness  which  shall 
correspond  to  that  between  less  and  more  negligible 
vagueness,  and  yet  not  depend  upon  it,  are  en- 
couraged instead  of  discouraged  by  the  traditional 
Logic,  and  chiefly  by  means  of  its  abstract  distinc- 
tion between  '  univocal  *  (straightforward)  and  *  equi- 
vocal '  (indefinite  or  ambiguous)  terms.  Naturally, 
if  the  only  distinction  that  can  be  made  between 
more  and  less  definite  words  is  unsatisfactory  we  can 
hardly  improve  matters  by  adding  a  fictitious  sharp- 
ness and  rigidity  to  its  other  defects.  Such  a  dis- 
tinction would  no  doubt  be  of  the  utmost  value  if 
w^e   could    reallv    draw^    it    otherwise    than     in    the 


*  This  question  is  discussed  in  Part  III. 
a  See  g  60. 


cH.  VH,  §42  INDEFINITENESS  AND  AMBIGUITY  183 

abstract ;  but  to  admit  this  is  by  no  means  to  admit 
that  it  can  be  so  drawn,  or  even  that  it  is  worth 
while  to  get  as  near  to  it  as  possible.  That  it  cannot 
be  more  than  abstract  follows  from  our  admission 
that  all  actual  names  are  indefinite ;  and  the  argu- 
ment against  neglecting  this,  as  a  finicking  kind  of 
truth,  and  doing  our  best  to  make  the  distinction  as 
little  misleading  as  possible,  is  what  we  are  now 
engaged  upon.  The  conclusion  we  are  to  reach  is 
that  the  only  way  to  destroy  its  misleading  power  is 
to  cease  from  attempting  to  use  it, — to  recognise  its 
defects  instead  of  glossing  them  over,  and  to 
substitute  for  the  conception  of  faulty  and  faultless 
words  that  of  ambiguous  and  unambiguous  asser- 
tions. 


8  42. — The  Indecision  of  Common  Sense 

That  some  reform  in  this  matter  is  needed  may  be 
seen  not  only  from  the  above  direct  criticism  on  the 
notion  of  greater  and  less  definiteness,  but  from  the 
contradictions  and  perplexities  which  are  traceable  to 
that  notion.  Although  in  the  main  its  effect  is  to 
discredit  careful  inquiries  into  a  definition,  yet  it  also 
weakens  our  power  of  dealing  effectively  with  those 
inquiries  when  they  are  really  quibbles.  On  the 
general  question  what  effect  '  indefiniteness  or 
ambiguity'  has  upon  meaning,  common  sense  can 
only  give  a  hopelessly  undecided  answer  ;  it  wavers 
between  the  view  that  a  '  slightly  ambiguous '  mean- 
ing is  better  that  none  at  all,  and  the  opposite  view 
that  if  you  pretend  to  use  a  word  with  a  meaning 
you  must  be  prepared  to  explain  exactly  what  you 
mean.      And  instead  of  clearly  recognising  the  self- 


184  USE  OF  WORDS  IX  REASONING       paktii 

contradiction  of  these  views  when  taken  as  general,  and 
setting  to  work  to  distinguish  the  one  kiiid  of  occasion 
from  the  other,  common  sense  is  content  to  leave  the 
two  views  side  by  side,  and  in  practice  to  appeal  to 
whichever  happens  to  be  convenient.      If  you  want 
to  defend  an  aniluguous  assertion,  you  find  it  useful 
to  remember  that  a  little  indefiniteness  is  not  a  serious 
matter ;  if  you  want  to  attack  one,  then  you  call  to 
mind  the  opposite   principle.      And   the    traditional 
Logic  makes  no  attempt  to  solve  this  difficulty  or  to 
deal  with  this  contradiction.     Hence  the  confusion  is 
not  confined   to  the  casual   opinions  of  the  average 
man,  but  a  good  deal  of  it  may  l)e  found  also  among 
philosophers,  if  their  views  on  this  particular  j)oint 
were  given   by  early  instruction,  and   have  happened 
not   to  advance   with    the   rest  of  their   knowledge. 
The  textbooks  dwell  only  on  the  kind  of  doubleness 
of  meaning  whicli   is  most  obvious.      For  instance,  if 
the    word   sovereiij.t    were   (chosen   to    illustrate  am- 
biguity, the  student  would  be  led  to  think  that  its 
defect   consisted    in    its    indifferent    applirability    to 
kings  and  coins}     The  (consequence  is  an  ini^rained 
idea  that  ambiguity  is  a  defect  that  only  the  most 
careless  assertions  can  suffer  from.      Naturally  (and 
often   rightly)  a  disciple   will   not   believe    that    his 
master's   doctrines  are   careless;    hence  the   deepest 
kmd  of  (criticism  of  these  doctrines  appears  to  him 
the  shallowest,  and  he  will  scarcely  listen  to  it.     Try 
tlie  experiment  with  the  disciples  of  any  writer  whose 
thought  here  and  there  rises  into  obscurity,  and  see 
what  proportion  of  them  will  stand  the  trial.- 

»  See  the  examples  given  by  Jevoiis  in  his  Elcnentaru  Ltssoiis,  iv.     See 
also  §  45  below. 

.v  'J^^:  f'"''''  ^'^"''^'  ''*'*•  ^^^°)  '^^'"^  ^«  ^^'ish  the  exiwriment  triwi  with 
the  disciples  of  T.  H.  (Jreen.     There  could  Iiardly  be  a  better  example. 


CH.  VII,  ^43  INDEFINITENESS  AND  AMBIGUITY  185 

Finally,  in  addition  to  the  other  reasons  against 
confusing  ambiguity  wdth  mere  indefiniteness  we 
should  notice  the  tendency  of  this  confusion  to  hide 
from  us  the  fact  that  all  descriptive  words  are  of 
necessity  indefinite.  What  common  sense  really 
rebels  against  admitting  is  that  descriptive  words  are 
always  ambiguous.  Everyone  sees  at  once  that  words 
are  not  in  fact  ambiguous  when  they  are  understood, 
and  that  this  fortunate  fate  sometimes  attends  them. 
Hence  no  one  who  means  by  *  indefinite '  the  same  as 
he  means  by  *  ambiguous '  can  admit  the  indefinite- 
ness of  all  class -names.  In  the  same  way  the 
comfortable  assumption  that  sin  essentially  consists 
in  being  found  out  may  hinder  our  conviction  that 
all  men  are  sinners. 


§  43. — Indefiniteness  as  Distinct  from 

Ambkjuity 

The  remedy  for  this  state  of  things  seems  to  be,  as 
we  said  just  now,  to  substitute  for  the  notion  of 
univocal  and  equivocal  (or  more  and  less  definite) 
words  that  of  ambiguous  and  unambiguous  assertions  ; 
to  substitute,  that  is,  for  the  popular  view  that  some 
words  are  so  indefinite  as  to  cause  important  confu- 
sion, while  others  are  so  definite  as  to  escape  this 
liability,  the  clear  recognition  that  all  words  are  alike 
indefinite  but  are  not  alike  ambiguous — the  latter 
defect  being  due  not  to  the  words  in  themselves  but 
to  the  occasions  of  their  use.  In  this  conception  are 
involved  the  following:  views :  that  indefiniteness  is 
not  itself  ambiguity,  but  is  only  a  predisposing  condi- 
tion of  it ;  that  ambiguity  arises  only  when  indefinite- 
ness  is  detected   in    a  special  context, — so  that  the 


186 


USE  OF  WORDS  IN  REASONING       part  ii 


opposition  resembles  that  between  fallibility  and 
detected  error ;  that  effective  doubtfulness  of  applica- 
tion is  not  a  quality  attaching  to  names  apart  from 
their  context,  but  only  belongs  to  them  as  actually 
used  in  assertions  ;  and  that  every  word,  in  spite  of  its 
fundamental  indefiniteness,  and  in  spite  of  any  varia- 
tions of  definiteness  which  (in  any  sense  whatever)  we 
may  choose  to  recognise  between  different  words,  is 
free  from  useful  doubt  in  some  of  its  applications,  and 
open  to  useful  doubt  in  others. 

It  may  be  suggested  that  the  question  as  to  a 
difference  between  indefiniteness  and  ambiguity  is  a 
mere  question  of  words.  We  should  admit,  of  course, 
that  the  choice  of  words  to  mark  an  opposition  is 
always  a  matter  of  pure  convenience,  and  is  therefore 
less  important  than  the  recognition  of  the  distinction 
by  means  of  some  words  or  other.  It  is  quite  possible 
that  by  means  of  some  such  expressions  as  actual  and 
potential  ambiguity,  or  effective  and  ineffective  in- 
definiteness, the  main  object  would  be  secured.  On 
the  whole,  however,  it  seems  more  convenient  to  say 
that  indefiniteness  when  detected  in  a  special  context 
becomes  ambiguity  (with  disastrous  effects  on  mean- 
ing), and  that  till  it  is  so  detected  it  remains  *  mere 
indefiniteness '  and  leaves  the  meaning  intact.  One 
reason  for  adopting  this  mode  of  expression  is  that 
the  common  confusion  is  no  doubt  partly  due  to 
insufficient  attempts  to  define  the  term  *  ambiguity.' 
The  most  superficial  account  that  could  be  given 
would  be  that  ambiguity  is  *  double  meaning,'  or  that 
"  a  word  is  ambiguous  when  it  has  more  than  one 
meaning,  as  for  instance  the  word  pound,  which 
means  indifferently  a  certain  coin,  a  certain  weight, 
and  a  pen  for  strayed  cattle."     Whatever  may  be  the 


CH.  vn,  ii  44  INDEFINITENESS  AND  AMBIGUITY  187 

merits  of  this  account  as  a  mere  translation  there 
could  scarcely  be  a  surer  way  of  obscuring  the  problem 
as  to  the  effects  of  ambiguity  than  by  taking  as 
typical  those  cases  which  are  least  effective  because 
the  double  meaning  is  most  obvious  and  well  known. 
Another  reason  for  making  the  distinction  between 
indefiniteness  and  ambiguity,  instead  of  between  two 
kinds  of  either,  is  that  the  well-intentioned  old  rule 
against  allowing  the  middle  term  of  a  syllogism  to  be 
ambiguous  evidently  does  not  recognise  any  harmless 
kind  of  ambiguity,  while  the  equally  well-intentioned 
rule  that  a  definition  must  not  be  expressed  in  in- 
definite language  evidently  allows  no  room  for  a  harm- 
less kind  of  indefiniteness.  The  former  rule  tells  us  that 
an  ambiguous  middle  always  invalidates  the  conclu- 
sion, and  not  only  when  the  middle  term  suffers  from 
one  particular  kind  of  the  defect ;  and  the  latter  rule 
sets  up,  as  we  have  seen,  a  wholly  impossible  standard, 
on  any  interpretation  except  that  *  indefinite '  means 
'  insufficiently  definite,'  and  thus  refers  to  the  special 
purpose  for  which  the  definition  is  wanted. 


S  44. — Ambiguity  as  Attaching  to  Assertions 

Assuming,  then,  that  we  consistently  substitute  for 
the  notion  of  perfect  and  imperfect  that  of  sufficient 
and  insufficient  definiteness,  and  also  reserve  the  term 
ambiguity  for  the  latter  of  these  two  conditions  of  a 
word,  it  is  easy  to  see  that  ambiguity  is  a  defect 
attaching  not  to  words  in  isolation  from  their  context, 
or  in  a  sort  of  average  context,  but  to  words  as  used 
in  asserting,  and  so  to  the  assertion  instead  of  to  the 
word.  The  convenience  for  the  sake  of  which  we  may 
sometimes  speak  of  '  ambiguous  words '  is  only  that 


i 


188 


USE  OF   WOllDS  JX  IlEASOMXCr        part  ii 


kind  of  convenience  which  justifies  any  loose  elliptical 
expression  when  a  longer  one  would  be  safer.  The 
common-sense  view  depends  upon  an  assumption  that 
words  are  things  which  exist  independently  of  their 
particular  context.  So  they  do, — in  a  dictionary,  or 
in  a  list  of  examples.  But  we  are  now  speaking  of 
the  conditions  of  the  use  of  language  ;  we  are  tryino" 
to  get  a  view  ol  words  and  assertions  not  as  they  look 
when  they  are  cut  and  dried  and  exhibited  in  a 
museum,  hut  as  they  grow  and  Hourish  or  wither, 
succeed  or  fail,  when  they  are  used  to  express  a  meaning. 
In  asking  whether  a  meaning  holds  or  fails  we  do  not 
necessarily  care  to  know  whether  most  people  on  most 
occasions  think  they  understand  the  words  or  not ; 
the  decisive  ijuestion  is  whether  on  the  given  occasion 
the  words  perform  their  function  properly.  That  is 
why  we  here  dwell  on  the  distinction  between  a  fault 
which,  like  aml)iguity,  attaches  lo  the  assertion,  and 
a  fault  which,  like  mere  indefiniteness,  attaches  to  the 
separate  words.  Tlie  faults  of  an  isolated  word  are 
often  irrelevant  in  a  given  context ;  there  are  manv 
cases  where  no  further  explanation  of  a  word  is  called 
for.  But  if  a  word  actually  produces  an  ambiguity 
some  further  explanations  are  then  imperatively  re- 
quired, for  without  them  the  statement  has  ceased  to 
l)e  an  assertion  at  all. 

Here  the  analogy  of  the  unwholesome  food  may 
be  referred  to  again.  For  ordinary  purposes  we 
habitually  assume  that  unwholesomeness  is  a  quality 
which  exists  simply  in  the  food,  not  in  the  food  and 
its  consumer  taken  together.  But  in  strictness  we 
know  that  the  fact  is  otherwise, — that  the  individual 
consumer  is  part  of  the  *  context '  of  any  given 
food,  and  that  its  actual  wholesomeness  depends  upon 


CM.  vn,  iU  INDEFINITENESS  AND  AMBIGUITY  189 

its  context.  We  must  not  press  the  analogy  too  far, 
but  we  may  notice  that  a  logician  who  declines  to 
take  the  context  of  words  into  account,  and  so 
declines  to  recognise  that  the  same  word  may  be 
sutticiently  definite  in  one  context  and  not  in 
another,  is  in  the  position  of  a  doctor  who  should 
hold  that  the  digestibility  of  a  given  kind  of  food 
is  something  quite  independent  of  the  person  who 
tries  to  digest  it.  Such  a  doctor,  we  must  admit, 
would  take  an  easy-going  view  of  the  science  of 
medicine. 

When  it  is  once  recognised  that  every  descriptive 
name  is  of  doubtful  application  in  some  cases  though 
sufficiently  safe  in  others,  we  have  taken  a  long 
step  towards  solving  the  problem  how  to  distinguish 
between  the  legitimate  or  useful  and  the  quibbling 
or  pedantic  inquiry  for  a  clear  definition  ;  for  then 
we  l>ase  the  value  or  need  of  the  inquiry  not  on  the 
sort  of  word,  considered  broadly,  nor  on  its  general 
utility,  but  on  its  actual  defect, — on  the  hindrance 
it  presents  to  Ijhe  desire  to  understand  sufficiently 
some  assertion  in  which  the  word  is  used.  We  have 
then  done  something  at  least  to  break  with  the  idea 
that  words  of  some  particular  kind, -for  instance 
the  words  that  *  everybody  knows  the  meaning  of* 
(like  horse),  or  again  those  that  admit  of  a  strict 
definition  (like  gold),  or  again  those  that  are  care- 
fully defined  for  special  purposes  (like  alien,  city, 
or  .£.'7  note) — are  thereby  safe  against  all  practical 
doubts  about  their  correct  application  in  particular 
cases ;  and  have  substituted  for  this  highly  mis- 
leading notion  that  of  requiring  to  know  what  a 
speaker  means  by  a  given  assertion  before  we  rush 
into  its  admission  or  denial. 


190 


USE  OF  WORDS  IN  REASONING       part  ii 


§  45. — Proportion  of  Doubtful  Applications 

Irrelevant 

In  the  same  way  we  get  rid  of  the  notion  that 
mere  number — or  proportion  between  the  safe  and 
the  doubtful  applications  of  a  given  word — has  any- 
thing to  do  with  the  question  whether  a  particular 
inquiry  is  justified,  except  to  prejudice  it.  This  is, 
in  fact,  almost  a  corollary  from  the  admission  ^  that 
obvious  sources  of  error  are  comparatively  in- 
effective ;  so  that  if  we  were  content  to  sort  out 
the  names  which  are  most  often  wrongly  or  doubt- 
fully applied,  and  to  regard  them  as  the  chief  source 
of  ambiguity,  we  should  only  have  found  the  source 
of  those  confusions  which  because  they  are  most 
noticeable  have  least  practical  importance.  The 
more  exceptional  any  source  of  confusion  is,  the 
more  difficult  it  is  to  guard  against  or  remove ;  and 
therefore  the  names  w^hose  defects  it  is  most  im- 
portant that  we  should  recognise  are  precisely  those 
in  which  the  defects  are  so  seldom  visible  that  we 
carelessly  take  them  as  *  for  practical  purposes '  non- 
existent. Practical  purposes  cannot,  except  in  the 
roughest  way,  be  lumped  together  as  an  indivisible 
whole. 

But  perhaps  an  instance  will  best  show  what  is 
meant.  Take  the  name  sovereign  (applied  to  a 
coin) — a  fairly  extreme  case  of  a  name  which  every- 
body knows  the  meaning  of,  and  which  also  admits 
of  close  definition,  both  chemically  and  by  more 
external  marks.  We  may  assume,  I  think,  that  the 
number  of  real  sovereigns  in  circulation   is  largely 

»  Page  180. 


CH.  VII,  §45  INDEFINITENESS  AND  AMBIGUITY  191 

in  excess  of  the  false  ones ;  for  which  reason  we 
commonly  accept  sovereigns  and  pass  them  on 
without  any  very  careful  reference  to  the  marks 
required  by  the  definition.  Yet  when  a  doubt  has 
actually  arisen  in  a  particular  case,  how  do  we  deal 
with  it?  Do  we  then  refer  to  the  mere  relative 
number  of  good  and  bad  sovereigns  as  having  any- 
thing to  do  with  the  matter?  Because  so  many 
millions  of  sovereigns  are  genuine  do  we  therefore 
accept  a  single  one  which  seems  suspiciously  light  ? 
Even  the  purely  business  man,  the  man  least  tainted 
by  logical  theory,  would  hardly  consider  that 
practical. 

It  is  true  that  in  the  case  of  doubtfully  genuine 
coins  the  man  of  business  does  not  himself  go  deeply 
into  the  definition.  But  that  is  because  a  rougher 
test — such  as  ringing  the  coin  on  a  counter — is 
generally  allowed  to  settle  the  matter,  while  if 
necessary  a  more  careful  expert  opinion  can  be 
taken.  Our  point  is,  not  that  the  practical  man 
himself  gives  much  elaborate  thought  to  the  question, 
but  that  instead  of  settling  it  on  statistical  grounds 
he  takes  the  doubtful  case  on  its  own  merits.  He 
does  not  think  it  unimportant  merely  because  it  is 
exceptional.  He  does  not  seek  excuses  for  avoiding 
the  inquiry  altogether,  but  settles  it  as  well  as 
circumstances  permit.  That  is  all  that  we  need 
here  recognise. 

Now  let  us  see  what  the  notion  of  taking  a  case 
on  its  own  merits  involves  in  regard  to  ambiguity 
generally.  Ambiguity,  as  we  have  defined  it,  arises 
where,  owing  to  some  hitherto  unnoticed  indefinite- 
ness  in  a  word,  an  assertion  in  which  that  word 
occurs  comes  under  suspicion  of  being  subtly  false. 


192 


USE  OF   WORDS  IN  REASON fNQ       partii 


The  purpose,  then,  for  which  the  definition  has  to  be 
sufficient  is  that  a  particular  assertion   sluill  have  a 
particular  doubt  as  to  its  meaning  removed.     And  to 
take  this  question  on  its  own  merits,   is  merely   to 
recognise  that  however  many  other  assertions,  some- 
thing  like   the    doubtful    one,    escape   the    need    for 
further  explanation,  they  no  more  affect  its  doubtful- 
ness than  the   millions  of  genuine  sovereigns  affect 
the  doubt  in  the  single  suspicious  case.      For  example 
we  may  raise  no  difficulty  about  understanding  the 
assertions    that    Brown,    and    Jones,    and    Robinson 
are  *  honest,'  but  when  we  come  to  the  case  of  Smith 
we  discover   a    difhculty  in  placing  him  clearly  on 
either  side  of  the  line.     That  difficulty  is  nothing  else 
than  the  difficulty  of  knowing  the  meaning  given  to 
the  word    in    this   particular  assertion.     We  might, 
for  instance,    agree    to  mean    by  Smith's  '  honesty  * 
that  no  shady  transactions  could  be  legally  proved 
against  him,  or  that  he  is  *  honest  according  to  his 
lights/  or  a^rain  that  he  is  about  as   honest    as  the 
majority    of   his   neighbours  or  the   average    of  his 
trade    or   profession.       But    some    agreement    there 
must  be,  some  choice  must  V)e  made  among  possible 
meanings  as  soon  as  we  see  that  different  meanings 
are   possible,   and    affect  the   answer.      Tacit   agree- 
ments of   this  kind    may    carry   us  far   in   common 
intercourse,  but  they  are  often  extremely  incomplete ; 
notoriously,  they  exist  sometimes  in  the  mind  of  the 
speaker   and  not  in  the  mind  of  his  audience,  and 
even  a  slight  difference  of  understanding  about  them 
may    be    enough    to    justify    the    inquiry    after    a 
definition. 

Those,  then,  are  the  sole  conditions  of  ambiguity, 
and  at  the  vsame  time  of  the  justified  demand  for 


™ 


I 


I 


cii.  VII,  H6  INDEFINITENESS  AND  AMBIGUITY  193 

further  definition  ;  there  nmst  be  an  assertion  pro- 
posed for  acceptance — a  question  raised — such  that 
if  it  be  taken  to  mean  one  thing  we  answer  Yes, 
while  if  it  be  taken  to  mean  another  we  either 
answer  No,  or  at  least  find  difficulties  in  the  way  of 
acceptance.  The  justification  of  the  demand  to 
know  which  meaning  is  intended  lies  partly  in  our 
desire  to  answer  intelligently  and  truthfully,  and 
partly  also  in  the  assumption  —  often,  no  doubt, 
ironical  —  that  the  assertor  himself  has  made  up 
his  mind  which  of  the  two  meanings  he  intends,  and 
lias  courage  to  let  the  decision  be  known.  I  speak 
here  of  assertor  and  audience,  as  if  they  were  neces- 
sarily two  different  people,  but  that  is  only  a  con- 
venient mode  of  expression,  corresponding  to  the 
case  where  the  confiict  is  most  visible.  In  strict- 
ness, however,  there  is  no  doubt  that  the  same 
process  of  forcing  further  definition, — and  even  of 
attempting  to  shirk  the  labour  of  it,  or  the  vaguely 
apprehended  consequences — goes  on  within  the  in- 
dividual mind.  In  fact,  as  we  shall  see,  the  growth 
of  knowledge  is  everywhere  conditioned  by  the 
view  of  the  need  for  further  definition  ;  it  is  always 
newly -seen  cases  of  difficulty  which  help  us  to 
correct  our  older,  slacker  generalisations  ;  everywhere 
it  is  the  unexpected  exceptions  which  test  and 
improve  our  hitherto  accepted  rules,  and  so  increase 
our  store  of  f];eneral  knowledge. 

§  46. — Subtlety  of  the  Inquiry  Irrelevant 

It  should  be  evident  now  that  the  subtlety  of  the 
inquiry  has,  in  itself,  nothing  to  do  with  the  dis- 
tinction between  the  inquiries  which  are  practically 

13 


194 


USE  OF  WORDS  IX  REASOXIXG       part  ii 


important  and  those  which  are  not  so.  The  need 
for  decision  between  two  meanings  in  order  that  an 
intelligent  choice  may  l)e  made  between  the  answer 
yes  and  no  is  something  which  is  totally  independent 
of  the  place  on  the  scale  of  careful  assertion  at  which 
the  need  happens  to  arise.  It  arises,  no  doubt, 
oftener  in  the  case  of  careless  assertions  than  of 
careful  ones ;  but  that,  we  have  seen,  is  an  irrelevant 
circumstance.  That  it  may  arise  in  the  case  of  the 
most  careful  assertion  follows  from  the  admission 
that  all  class-names  are  indefinite.  The  definiteness 
of  a  name,  as  we  found,  can  never  mean  more  than 
sufficient  definiteness  ;  and  the  fact — if  it  ever  occurs 
— that  a  name  has  sufficed  even  m  nil  previous  cases 
to  express  assertions  which  are  free  from  ambiguity 
does  not  prevent  its  failing  on  the  next  occasion. 
The  most  we  can  ever  declare  with  safety  in  such  a 
matter  is  that  our  own  imagination  of  possible 
difficulties  in  applying  the  word  is  at  a  loss  ;  not 
only  can  w^e  never  l)e  sure  that  future  generations 
will  have  an  equally  limited  imagination,  but  it  may 
even  be  the  case  that  some  existing  people  have  a 
keener  foresight  of  difficulties  than  ourselves,  or 
are  more  inclined  to  take  the  requisite  trouble  to 
imagine  them.  Thus  we  cannot,  except  (piite 
roughly,  predict,  in  the  case  of  any  class  -  name, 
the  likelihood  of  its  escaping  the  normal  fate  of 
class-names  any  longer ;  the  utmost  value  of  such  a 
prediction  is  only  that  of  wisdom  before  the  event. 
— like  our  opinion  that  the  British  Em})ire  will  last 
another  fifty  years,  or  that  the  train  I  am  in  will 
reach  its  destination  safely.  Will  any  one  claim  that 
we  can  set  a  mere  prediction,  however  well  founded, 
against  the  subsequent  ev^ent  which  contradicts  it  ? 


c'H.  vir,  .^  47  IXDEFIXTTEXESS  AXD  AMBIGUITY  195 

Of  course,  so  far  as  the  event  itself  is  of  a  kind  which 
is  doubtful,  this  clash  between  previous  theory  and 
observed  fact  often  leads  quite  rightly  to  a  recon- 
sideration of  the  '  fact,'  and  so  to  a  discovery  that 
the  theory  is  not  yet  upset ;  as,  for  example,  in 
the  case  of  the  theory  that  acquired  characters  are 
not  transmitted  by  descent.  But  how  can  such  a 
conflict  ever  occur  in  the  case  of  a  seen  ambiguity  ? 
Can  a  man  see  an  ambiguity  and  at  the  same  time 
not  see  it  ?  Wonderful  acrobatic  feats  of  the  mind 
are,  no  doubt,  to  be  met  with,  but  would  not  that 
surpass  all  that  can  be  intelligently  imagined  ? 

8  47. — The  Work  involved  in  Finding 

AN  Ambiguity 

Its  impossibility  will  perhaps  be  even  clearer  if  we 
look  at  what  is  involved  in  finding  an  ambiguity. 
As  soon  as  we  recognise  that  perfect  definiteness  is 
a  chimera,  we  have  broken  of  course  with  the  idea 
that  there  is  any  virtue  in  asking  at  random  for 
more  and  more  definition,  insatiably.  We  have 
then  already  begun  to  see  that  the  mere  demand 
for  a  difficult  definition,  or  the  mere  complaint 
that  a  word  is  vague,  is  anything  ])ut  a  formidable 
controversial  weapon.  It  amounts  to  no  more  than 
accusing  an  assertor  of  being  fallible.  We  have 
then  already  begun  to  see  how  false  it  is — except 
ill  a  sense  that  does  not  matter — that  a  child  can 
raise  more  doubts  in  half-an-hour  than  a  sage  can 
answer  in  a  year ;  we  have  then  already  understood 
that  though  foolish  doubts  can  always  be  verbally 
raised  they  admit  of  being  very  easily  disposed  of, 
and   that   the  raising  of  valuable   doubts — ie.   the 


I 


t 

i 


19G 


USE  OF  WOllDS  IN  llEASONING       part  ii 


discovery  of  an  aml)iguity — is  anything  but  an  easy 
process.  But  its  ditficulty  becomes  more  evident  still 
when  we  consider  more  precisely  what  the  process 
involves.  The  recognition  of  two  different  mean- 
ings of  a  class-name  used  as  predicate  implies  the 
recognition  of  two  sub-classes  contrasted  with  each 
other ;  and  if  we  have  seen  that  one  of  the  meaninirs 
leads  us  to  answer  yes,  while  the  other  makes  us 
hesitate  or  answer  no,  that  implies  that  we  think  we 
know  something  about  the  difference, — that  we  have 
not  merely  noted  it  as  the  ground  of  a  possible  sub- 
division but  have  seen  something  at  least  of  what 
turns  upon  it. 

As  an  everyday  example,  of  a  simple  kind,  take 
the  name  Liberal  as  applied  in  English  politics. 
Towards  the  end  of  1885,  when  rumours  l)e<;an  to 
be  heard  that  the  Liljeral  leader  had  been  converted 
to  Home  Rule,  it  was  not  at  first  clearly  foreseen  how 
important  a  division  would  shortly  have  to  be  made 
within  the  ranks  of  the  party  as  then  constituted. 
It  was  assumed,  of  course,  that  the  name  covered  a 
certain  amount  of  individual  difl'erence  of  opinion, 
but  the  special  ambiguity  which  soon  after  arose 
was  then  still  in  the  womb  of  the  future.  The 
indefiniteness  which  was  latent  in  the  name  up  to 
the  beginning  of  April  1886  became  a  few  months 
afterwards  so  patent  as  to  cause  ambiguity ;  within 
what  used  to  be  called  the  Liberal  party  there  had 
come  to  light  two  sub-classes  each  of  which  denied 
to  the  other  the  right  to  the  name. 

What  happened  in  this  case  so  markedly  is 
happening  every  day,  more  quietly,  more  gradually, 
in  the  wake  of  all  discoveries  of  fact.  A  discovery 
of  fact  is  never  quite  without  importance,  and  what- 


CH.  VII,  .^  48  INDEFINITENESS  AND  AMBIGUITY  197 

ever  importance  it  has  is  class  importance  ;  it  affects 
not  only  an  individual  case  but  a  class  of  cases.  Its 
influence  upon  language  is  always  in  the  direction 
of  rendering  clumsy — rendering  plainly  indefinite — a 
name  wliose  indefiniteness  had  till  then  mven  no 
obvious  trouble. 

Since,  then,  the  discovery  of  an  ambiguity  implies 
the  discovery  of  an  apparently  important  subdivision 
to  l)e  made  within  a  class, — implies  therefore  that  we 
have  gone  forward  from  a  simpler  to  a  more  complex 
view  of  tlie  meaning  of  the  class-name, — the  possibility 
tliat  we  can  also  have  stood  still  and  not  done 
this  is  one  that  we  are  powerless  to  consider.  Of 
course  the  apparently  important  su1)division  may 
turn  out  to  be  unimportant,  but  that  recognition 
involves  the  removal  of  the  ambiguity  as  a  prior 
condition.  If  and  while  an  ambiguity  stands  in 
the  way,  then,  however  mistaken  may  be  the  views 
which  create  it,  the  only  path  lies  forward  through 
its  removal  and  not  back  to  the  unsuspecting 
innocence  we  enjoyed  in  the  earlier  stages.  There 
can  be  no  doubt  of  the  feeling  of  doubt  itself, 
especially  when  it  is  a  reasoned  doubt ;  when  it 
has  once  arisen,  that  occurrence  has  already  falsified 
the  prediction  that  it  would  never  arise. 

8  48. — Summary  of  the  Chapter 

In  this  chapter  we  have  been  discussing  certain 
points  which  bear  directly  upon  the  difference 
1  between  the  justified  and  the  unjustified  inquiry 
for  a  definition,  and  our  plan  has  been  to  examine 
some  views  about  it  which  are  prevalent  in  popular 
thought.      The  fact  that  they  are  also  encouraged 


198 


Ui^E  OF   won  US  IX  J:EASOMXa       PART  II 


\ 


by  Formal  Logic  gives  them  a  wider  range  of  harmful 
influence  than  tliey  might  otherwise  have,  and  makes 
it  more  worth  while  for  us  to  examine  their  defects. 
The  outcome  of  such  views  is  a  vacillatine:  answer 
to  the  question  wlien  a  closer  definition  is  required 
in  order  to  make  a  meaning,  an  answer  which  leaves 
the  question  undecided,  and  which  therefore  on  the 
whole  favours  the  easier  course  of  regarding  inquiries 
into  a  definition  as  justified  rather  hy  their  avoidance 
of  subtlety  than  by  the  nature  of  the  occasion  that 
raises  them.  It  is  always  easier  to  take  a  general 
nde  as  independent  of  special  occasions  than  to  enter 
into  the  inquiry  what  the  im{)ui  lance  of  its  exceptions 
depends  upon. 

The  general  rule,  then,  which  common  sense  is 
inclined  to  l)elieve  sufficient  is  that  inquiries  into  a 
definition  ought  to  be  stopped  at  the  point  where  they 
become  too  subtle.  Assuming  that  this  is  not  merely 
an  empty  phrase  meaning  that  they  ought  to  be 
stopped  just  at  the  point  where  they  ought  to  be 
stopped,  it  implies  the  assumption  that  certain 
degrees  of  indejiniteness  are  harmful,  but  that  in  all 
other  cases  it  is  better  to  make  light  of  the  defect 
and  not  to  press  for  definition.  A  difficulty  might 
be  found  in  settling  the  exact  line  between  the  two 
kinds,  but  there  is  no  need  for  us  to  dwell  on  this 
objection  since  another  one  claims  our  attention  first. 
The  whole  conception  of  degrees  of  indefiniteness  is 
faulty  from  the  beginning.  It  is  often  no  more  than 
a  softened  form  of  the  old  abstract  distinction  l)etween 
univocal  and  equivocal  terms,  wliich  involves  the 
false  assumption  that  some  words  are  perfectly  de- 
finite ;  but  even  if  we  take  the  conception  of  degrees 
as  not  involving  this  assumption,  still  it  cannot  be 


CH.  VH,  §  48  lyjJEFJXITEXESS  AND  AMBIGUITY  191> 

criven  a  meaning  such  that  the  more  indefinite  words 
shall  be  those  that  most  need  definition,  unless  we 
\)Q(f  the  question  and  make  the  degree  of  indefinite- 
ness depend  on  the  need.  At  least  we  found  reasons 
for  seeing  that  if  the  need  of  definition  is  to  be  in 
proportion  to  the  degree  of  indefiniteness,  then  the 
more  indefinite  words  cannot  l)e  those  which  are 
<a*ossly  and  obviously  indefinite,  nor  those  which  are 
least  carefullv  defined.  It  remains  for  any  one  wdio 
thinks  he  knows  what  the  distinction  can  mean  to 
give  some  acceptal)le  explanation. 

Even  if  the  false  assumption  that  some  words  are 
perfectly  definite  be  not  exactly  involved,  there  can 
l)e  little  doubt  that  the  slack  popular  view  just 
spoken  of  gets  much  of  its  supi)ort  from  an  incomplete 
recognition  of  tlic  necessary  indefiniteness  of  all  de- 
scriptive words.  For  that  reason  it  seemed  worth 
while  to  set  out  expressly  the  manner  in  which  this 
necessary  indefiniteness  is  derivable  from  the  necessary 
incompleteness  of  all  description,  and  how  that  again 
is  derivable  from  the  fact  that  general  names  (how- 
ever complex)  cover  individual  difierences.  But  the 
chief  source  of  failure  to  grasp  these  truths  and  to 
follow  out  their  consequences  consistently  is  to  be 
found  in  the  common  confusion  between  indefiniteness 
and  ambiguity,  due  partly  to  insufficient  definitions 
of  tlie  latter  word,  and  partly  to  the  ftital  habit — 
again  encouraged  by  Formal  Logic — of  considering 
words  apart  from  their  context,  and  so  of  trying  to 
explain  by  reference  to  the  nature  of  the  word  alone 
differences  which  belong  not  to  the  word  but  to  its 
use  in  different  particular  contexts.  Take  any  two 
predications  with  the  same  predicate  term,  and  one 
may  be  ambiguous  while  the  other  is  not,  though  in 


5t 

t 


200 


USE  OF  WORDS  IN  REASONING       I'Aiirir 


both  alike  that  predicate  term  is  incompletely  definite. 
When  Shakespeare  is  called  a  poet,  no  one  troubles 
about  the  definition  of  that  term ;  but  when  it  is 
applied  in  certain  other  cases  we  begin  to  ask  how 
far  it  may  be  legitimately  extended. 

From  all  these  considerations  we  found  that  the 
main  remedy  for  the  defects  of  the  popular  view  is 
to  keep  in  mind  the  distinction  here  drawn  between 
indefiniteness  and  ambiguity,  whether  we  use  those 
names  to  express  it  or  invent  others  which  we  may 
think  better.     Whatever  name  we  use  for  that  defect 
in  assertions — i.e.  in  words  as  used— which  is  to  be 
contrasted  with  indefiniteness  in  isolated  words,  the 
point  to  recognise  is  that  every  word,  however  definite 
or  indefinite  in   itself,  is  free  from  useful  doubt  in 
some  of  its  applications  and  open  to  useful  doubt  in 
others ;  and  that  when  one  of  these  latter  occasions 
comes  Ijefore  us  the  mere  number  of  the  safe  apjjlica- 
tions  is  not  a  relevant  circumstance,  since  they  are 
not  the  one  in  question.     Thus  we  are  not  asked  to 
regard   class-names   as   universally   unintelligible   or 
misunderstood,    but   only    to   refrain    from    another 
equally  unpractical  mental  habit, — namely  that   of 
declining  to  see  the  defect  in  an  assertion's  meaning 
because  numbers  of  other  assertions,  something  like 
It,  escape  that  defect.      The  others  have  the  same 
predicate  term  but  a  difl'erent  Subject ;  and  it  is  the 
difference  in  the  Subject  which  alone  occasions  the 
doubt.     So  that  the  logical  doctrine,  expressed  more 
generally,  is  negative  in  character.     It  does  not  say 
that  particular  doubts  should  be  raised ;  l)ut  merely 
that,  being  raised,  they  cannot  in  the  name  of  Logic 
be   stifled   without    investigation.      A   given   doubt 
raised  in  a  case  of  assertion  cannot  be  dismissed  on 


OH.  VII,  §48  INDEFINITENESS  AND  AMBIGUITY  201 

the  ground  that  '  every  one  knows '  what  is  meant 
by  the  word  which  suggests  the  doubt ;  or  that  in  all 
but  a  tiny  percentage  of  cases  that  word  is  applied 
with  ease  and  correctness  by  all  the  world.  Such  a 
fact  is  irrelevant  supposing  an  actual  doubt  to  have 
already  arisen.  At  most  it  means  that  confusion  does 
not  seem  likely ;  it  tells  us  nothing  as  to  whether  an 
important  confusion  has  in  fact  been  made. 

Only  in  this  way  can  we  get  the  harmlessness  of 
mere  indefiniteness  clearly  contrasted  with  the  harm 
of  aml)iguity,  and  see  precisely  what  eSect  the  latter 
has  upon  meaning.  We  then  find  that  so  long  as  a  dis- 
covered ambiguity  remains  unremoved  the  meaning  of 
the  assertion  in  which  it  occurs  has  totally  disappeared. 
It  may  of  course  be  loosely  called  a  '  vague  assertion,' 
l)ut  it  differs  from  those  vague  assertions  which  are 
merely  incomplete — as  all  assertions  must  be — in  the 
fact  that  it  is  challenged  in  a  particular  point.  There 
are  two  senses  suggested  and  the  assertor  is  requested 
to  choose  between  them,  on  the  ground  that  until  he 
iloes  so  there  is  nothing  about  which  issue  can  be 
joined.  Taken  in  one  sense  the  assertion  gives  only 
stale  information,  and  has  therefore  to  that  particular 
audience  no  interest ;  and  until  the  audience  knows 
whether  it  is  to  be  taken  in  the  other  sense  or  not, 
there  is  nothing  proposed  for  their  consideration. 
In  such  cases  they  can  only  wait  for  further  explana- 
tions, and  in  supplying  them  the  assertor  can  give 
a  kind  of  help  that  no  one  else  can  give, — that  is  to 
say,  if  he  is  desirous  of  making  a  meaning.  He  can 
choose  whether  to  leave  his  statement  in  its  present 
empty  condition  or  to  take  the  risk  of  saying  some- 
thing which  may  be  disputed.  Thus  ambiguity  does 
not  merely  spoil  some  ideal  perfection  of  meaning 


m 


4< 


202 


USE  OF  WOIIDS  IN  IlEASOXIXG       part  ii 


wliicli  a  pedant  may  stickle  fur,  or  a  sophist  make  a 
point  of  demanding,  l)ut  destroys  just  that  practical 
meaning  or  value  which  every  assertion,  as  such,  is 
bound  to  have. 

The  most  direct  Ijearing  of  these  considerations  is 
on  questions  which  arise  in  the  course  of  controversy, 
where  one  party  is  more  confused,  or  more  inclined  to 
crooked  ways,  than  the  other ;  though,  as  will  appear 
in  next  chapter,  this  is  not  their  only  bearing.     So 
far  as  controversy  is  concerned,  however,  w^e  have 
now  seen  how  it  is  that  the  practice  of  demanding 
definitions  plays  so  large  a   part  as  it  does  in   all 
disputed  questions.      xVmbiguity  is  fatal   to  a  clear 
issue,  and  is  only  to  be  removed  l)y  means  of  defini- 
tion ;  definition   is  thus  tlie  chief  instrument  in  the 
process  of  getting  an  issue  clear  and  so  takino-  the 
first   step   towards    reducing    diHcrences    of   opinion. 
And  so  long  as  any  difference  of  opinion  remains — 
so  long  as  the  process  of  reaching  agreement  can  be 
carried  further— the  same  operation  is  still  needed  in 
more  and  more  subtle  forms;   for  all  disputes  may, 
as  we  saw,^  be  in  the  end  resolved   into  the   doubt 
whether  this  or  that  su[)posed  case  of  P  really  deserves 
the  name.     So  that  all  through  the  process  of  reduc- 
ing difterences  of  opinion,  from  the  most  hot-headed 
antagonistic  stage  down  to  a  *  question  of  lact '  ad- 
mitted as  such   by  l)oth  the  opposite   parties,  both 
fairness  and  success  depend  on  our  knowin^^  clearlv 
when  and  why  definitions  may  ])e  demanded ;  upon 
our  knowing   what   names,   on   what  occasions,   can 
need  to  be  defined.      In  all  disputes,  during  the  pro- 
cess of  reduction,  the  (juestion  is  liable  to  arise,  which 
of  the  two  parties  is  evading  the  issue, — the  critic  who 

»   Pp.  106,  l:J6,  lis. 


CH.  VII,  H^  INDEFIXITEXESS  AXD  AMBIGUITY  203 

demands  a  definition  or  the  assertor  who  fails  to  meet 
the  demand;  the  question  whether  the  demand  is 
irrelevant  or  whether  the  failure  of  definiteness  entirely 
or  only  partly  destroys  the  meaning  of  the  assertion. 
This  question  cannot  be  intelligently  answered  so  long 
as  ambiguity  is  supposed  to  be  the  same  thing  as 
indefiniteness,  or  to  differ  from  it  only  in  degree. 

It  should  now  be  evident  that  the  demand  for  a 
definition  gets  its  justice,  and  its  effectiveness  as 
a  controversiaUveapon,  entirely  from  its  reference  to 
a  particular  assertion  made.  The  whole  distinction 
between  the  just  demand  and  the  quibbling  demand 
turns  on  the  question  of  the  particular  reference. 
Words  with  a  descriptive  meaning,  when  taken  apart 
from  the  assertions  in  which  they  occur,  are  always 
indefinite,  or  capable  of  creating  an  ambiguity,  but  it 
is  only  when  they  have  actually  done  so — and  there- 
fore when  they  are  considered  in  reference  to  their 
special  context — that  their  indefiniteness  has  any 
effect  on  the  meaning.  And  the  effect  it  then  has  is 
absolutely  destructive  until  the  ambiguity  is  removed. 

It  should  also  be  evident  that  when  an  ambiguity 
has  been  discovered,  its  removal  is  always  an  easy 
matter  if  the  assertor  really  has  a  meaning  and  is  will- 
ing to  let  it  be  known.  The  worst  of  it  is  that  assertors 
often  find  it  still  easier,  or  in  some  way  more  satisfac- 
tory to  themselves,  not  to  confess  to  a  definite  mean- 
ing but  rather  to  shift  about  between  two  meanings 
one  of  which  is  safer  from  attack  than  the  other.  When 
a  statement  is  felt  to  be  difficult  to  defend  there  are 
often  strong  inducements  not  to  admit  the  difficulty, 
but  rather  to  pretend  or  assume  that  it  does  not 
exist.  Against  a  critic  properly  armed  the  shifty 
assertor  cannot  succeed  in  this  attempt,  but  he  often 


204  USE  OF   WORDS  IN  REASONING       PARTir 

thinks  it  worth  while  to  try,  or  at  any  rate  gives 
the  plan  a  trial  without  much  thought.  Under  all 
variations  his  mode  of  operation  is  then  the  same  : 
the  assertion  he  defends  is  not  the  assertion  attacked, 
but  (if  he  is  skilful)  one  so  nearly  like  it  as  to  be 
easily  mistaken  for  it.  And  the  only  remedy  is  to 
make  the  difference  clear. 

But,  as  we  are  now  to  notice,  the  bearing  of  these 
considerations  upon  the  tricks  of  controversy  is  onl}' 
a  part  of  their  service. 


CHAPTER  VIII 


THE    PROGRESS   OF    KNOWLEDGE 


§  49. — Questions  of  Fact  and  of  Meaning 

In  §  45  we  referred  to  the  statement  *  Here  is  a 
sovereiiin '  as  an  instance  of  the  use  of  a  name 
which  miglit  cause  ambiguity  in  spite  of  its  definition 
being  so  wxU  known  for  practical  purposes  as  to  give, 
on  the  whole,  very  little  trouble.  This  instance,  it 
will  be  remembered,  was  chosen  as  a  fairly  extreme 
case  of  a  word  which  everybody  knows  the  meaning 
of,  and  it  was  admitted  that  ambiguity  is  at  present 
quite  unlikely  to  arise  out  of  it.  Evidently  the 
question  whether  an  apparent  sovereign  is  really  a 
sovereign  or  not  is  more  naturally  viewed  as  a 
question  of  fact — as  a  question  whether  the  particular 
coin  is  heavy  enough,  hard  enough,  and  rings  clearly 
— than  as  a  question  of  the  precise  meaning  of  the 
word.  The  unlikely  case  in  w^iicli  it  could  lead  to 
ambiguity  would  arise  only  if  the  now  accepted  tests 
should  lose  their  value, — if,  for  instance,  some  in- 
ingenious  chemist  were  to  find  out  how  to  make  '  real 
gold '  sovereigns  at  a  much  lower  cost.  At  present, 
however,  and  as  far  as  we  can  see  into  the  future, 
we  know  fairly  well  the  conditions  under  which  bad 
sovereigns   are    produced,    and   specially    that   they 


20G 


USE  OF  WORDS  IN  llEASOXIXG       paiit  ii 


cannot  be  made  at  a  profit  unless  they  are  made  of 
base  metal;  moreover  they  do  not  grow  old  or 
decay  rapidly  enough  to  cause  difficulty.  If,  for 
instance,  a  bad  sovereign  could  become  a  good  one  by 
necromancy,  or  if  sovereigns  were  apt  to  go  bad  in 
hot  weather,  the  defining  line  between  those  which 
are  worth  twenty  shillings  and  those  which  are  not 
would  at  once  l)ecome  a  source  of  the  most  practical 
trouble. 

The  distinction  between  questions  of  fact  and 
questions  of  meaning  (or  of  words,  or  of  defini- 
tion), is  one  which,  as  we  all  know,  is  often  referred 
to  in  arguments.  That  the  difference  is  not  as  a 
rule  very  clearly  apprehended  may  be  seen  from  the 
fact  that  the  parties  arguing  often  fail  to  discover 
the  verbal  character  of  the  question  until  the  dispute 
has  lasted  a  long  time.  Both  sides  commonly  begin 
by  supposing  that  the  point  at  issue  is  a  question  of 
fact;  and  then,  after  they  have  proceeded  on  this 
assumption  until  each  has  unl)ur(lened  liimself  of  his 
opinions,  suddenly  out  Hies  the  bottom  of  the  con- 
troversy and  the  opponents  become  aware  that  no 
facts  are  in  dispute  and  that  "  after  all,  it  is  only  a 
question  of  names."  And  then  their  wisdom  after 
this  event  usually  leads  them  to  think  that  the 
original  question  was  trivial;  they  fail  to  see  that 
the  clear  reduction  of  the  dispute  to  a  verl)al  one  is 
itself  a  step  gained  in  advance  of  their  former 
position. 

We  cannot  wonder,  however,  that  the  distinction 
between  questions  of  fact  and  questions  of  definition 
is  vaguely  apprehended  when  we  examine  its  nature. 
The  point  of  it  is  the  assumption  that  some  questions 
do,  while  others  do  not,  admit  of  misinterpretation ; 


CH.  vni,  §  49      THE  PEOGBESS  OF  KXO  W LEDGE     207 

which  is  again  the  untenable  assumption,  discussed 
in  last  chapter,  that  some  words  are,  while  others 
are  not, '  indefinite  or  ambiguous.'  Such  a  distinction, 
we  saw,  does  not  admit  of  any  careful  application ; 
and  it  tends  moreover  to  oljscure  the  connection  be- 
tween the  finding  of  ambiguities  and  the  progress 
of  knowledfje. 

What  is  it  that  makes  one  question  less  liable  to 
be  misinterpreted  than  another?  It  is  not  merely 
the  familiarity  of  the  words  in  which  it  is  expressed, 
for  no  words  are  more  familiar  than  the  epithets  of 
praise  and  blame  which,  more  often  than  any  other 
kind  of  words,  lead  to  confused  issues.  Nor  can 
it  be  the  simplicity  of  the  fact  itself,  for  that,  as 
we  have  seen,^  is  delusive.  And  if  we  make  the  dis- 
tinction one  of  degree,  saying  that  all  questions  below 
a  certain  degree  of  complexity  are  questions  of  fact 
while  all  al)ove  it  raise  questions  of  definition  before 
tlie  facts  can  be  decided,  then  we  get  into  precisely  the 
same  kind  of  difficulties  as  those  we  encountered  in 
§  4 1  al^out  the  assumed  degrees  of  indefiniteness.  If  all 
facts  are  infinitely  complex,  what  shall  be  meant  by 
degrees  of  complexity  ?  Can  we  give  the  phrase  any 
meaning  which  does  not  involve  the  circular  explana- 
tion that  questions  are  about  a  definition  where  the 
facts  are  sufficiently  complex,  while  the  sufficient 
complexity  of  the  facts  is  evidenced  by  the  felt  need 
for  disentangling  the  several  strands  of  possible 
meaning  ? 

But  if  we  make  it  turn  on  the  supposed  simplicity 
of  the  fact  in  question,  all  these  difficulties  disappear, 
and,  though  the  faults  of  the  distinction  itself  then 
come  to  light   more   clearly   than  before,  our  very 

»  See  §  13,  and  pp.  94,  173. 


4' 


208 


USE  OF  WOnnS  in  REA^^ONIXG       part  II 


recognition  of  them  helps  us  to  undei-stand  just  that 
source  of  progress  which  is  otherwise  left  obscure. 
Though  there  cannot  be  any  clear  opposition  between 
two  classes  of  question  on  the  ground  of  real  sim- 
plicity,  yet  on  the  ground  of  supposed  simplicity, 
or  seen  complexity,  it  is   plain   that   a   distinction 
of  degree  is  easily  possible.     Indeed,  whatever  prac- 
tical   value    the    distinction    has   evidently    lies    in 
marking  oft'  those   questions    which    may   he    taken 
as  simple  from  those  which  may  not.     For  various 
reasons,   among  which    economy  of  time  is   one  of 
the    most    important,   we    are   driven    to    recognise 
plenty  of  questions  which  are  never  likely  to   need 
carrying  up  into  the  region  of  difticulties  of  precise 
description,  since  they  are  sufliciently  answered  on 
a  less  philosophical  level ;    and   it   is  convenient  to 
group  them  together  under  the  common  designation 
*  questions  of  fact,'  so  as  to  keep  clearly  in  view  the 
suitable  means  of  answering;  them.     It  is  a  workin^i^ 
distinction,  analogous  to  that  which  is  made  in  our 
Law  Courts  between  what  is  '  evidence '  and  what  is 
not;  and,  like  all  working  distinctions,  it  is  sure  to 
lead  to  injustice  here  and  there  if  we  trust  it  abso- 
lutely.    Science,  with  more  time  at  disposal  than  the 
Law  Courts  have,  does  not  insist  on  any  hard  dis- 
tinction l)etween  what  is  evidence  and  what  is  not  ; 
that  particular  time-saving  apparatus   is   found  too 
untrustworthy  for   the   minutely    accurate   inquiries 
which  are  the  special  business  of  science.     And  loorjcal 
science  cannot  insist  on  any  sharp  distinction  between 
questions  of  fact  and  questions  of  definition.     Indeed, 
we  have  already  ^  gone  further,  and  recognised  that 
every  question  of  fact  is  a  question  of  theory  about  a 

»  §31. 


CH.  VIII,  ^  49      THE  PROGRESS  OF  KNO  WLEDGE     209 

fact ;  and  in  so  far  as  it  is  a  difficult  question,  not 
easily  reduced  to  a  simple  and  definite  test,  either 
itself  is  or  else  involves  a  question  as  to  the  proper 
application  of  some  class-name. 

When  we  have  once  recognised  that  questions  of 
definition  are  those  questions  where  the  point  at  issue 
is  seen  to  be  complex,  it  is  only  one  step  further  to 
the  recognition  that  since  all  men's  insight  into  com- 
plexities is  not  equal,  the  same  question  will  seem  to 
one  man  a  question  of  fact  while  to  another  it  will 
seem  to  require  preliminary  definition.  Though  there 
may  be  some  extreme  cases  on  either  side,  about 
which  no  difficulty  ever  arises,  there  are  evidently 
also  numerous  questions  that  are  taken  differently  by 
different  people. 

For  instance,  two  or  three  centuries  ago  the  ques- 
tion whether  God  exists  was  regarded  by  almost  every 
one  as  a  question  of  fact,  and  even  at  the  present  time 
there  must  be  millions  who  so  regard  it,  whatever 
shade  of  belief  or  disbelief  or  reservation  of  judgment 
they  profess  or  feel.  But  the  same  question  is  now 
seen  to  be  ambiguous  by  a  minority  who  have  allowed 
tliemselves  to  recognise  the  variety  of  the  meanings 
ill  which  it  may  be  taken.  Taken  as  Spinoza  took  it, 
assent  becomes  a  truism  ;  taken  as  the  Mahdi  or 
Oliver  Cromwell  took  it,  doubts  have  a  standing 
ground.  The  old  apparent  simplicity  of  the  question 
is  thus  giving  place  to  a  view  of  its  complexity,  and 
instead  of  remaining  confessedly  a  question  of  fact, 
like  the  (juestion  al)out  the  existence  of  a  hitherto 
unknown  planet,  it  is  beginning  to  be  taken  as  a 
question  whether  this  or  that  conception  of  the  Deity 
is  a  truthful  one, — the  conception,  for  instance,  that 
'God'   delights   in    burnt  offerings,   or   is   likely  to 

14 


210 


USE  OF  WORDS  IN  REASOMNG       part  ii 


wreck  a  Sunday  excursion  train.  The  scjlioolboy's 
answer  that  Homer  never  existed,  hut  only  some  one 
else  of  the  same  name,  marked  a  stage  intermediate 
hetween  taking  the  question  of  Homer's  existence  as 
simple  and  recognising  its  complexity. 

If  we  now  inquire  what  is  the  extent  of  this  inter- 
mediate class  of  questions,  which  are  questions  of  fact 
to  one  person  and  questions  of  definition  to  another, 
we  shall  find  it  very  difficult  to  put  a  limit  to  them, 
even  approximately.  The  limit  on  the  one  side  is 
fixed  pretty  clearly,  at  a  given  date,  ])y  the  fact  of 
no  ambiguity  having  yet  arisen— as,  we  will  assume, 
is  the  case  with  the  word  *  gold ' ;  or  as  a  few  years 
ago  was  the  case  with  the  words  '  diamond '  and 
*ruby,'  when  the  nearest  imitations  were  more  easily 
distinguished  from  the  real  ones  than  they  now  can 
be.  On  the  other  side,  however,  tlie  limit  seems 
quite  impossible  to  draw  except  in  a  high-handed 
way  which  is  foreign  to  the  spirit  of  philosophy.  It 
is  generally  easy  to  assume,  of  course,  that  those  who 
take  as  a  question  of  simple  fact  some  question  which 
we  ourselves  regard  as  verbal  are  people  who  need  not 
be  considered  ;  but  when  it  comes  to  attempting  to 
draw  a  clear  line,  on  any  such  basis,  between  questions 
of  fact  and  (questions  of  definition,  we  open  the  door 
to  some  very  troublesome  doubts  as  to  the  justice  of 
the  assumption  in  particular  cases.  Clearly  it  will 
not  do,  at  any  rate,  to  make  a  general  claim  to  settle 
such  doubts  out  of  hand, — it  would  not  conduce  to 
the  habit  of  truth -seeking,  but  rather  to  that  of 
neglecting  to  hear  opponents.  It  is  only  too  easy  to 
hold  the  view  that  our  opponents,  as  such,  are  people 
to  be  left  out  of  account. 

As  a  result  of  the  inquiry,  then,  how  to  distinguish 


CH.  VIII,  .^  49      THE  PROGRESS  OF  KNO  WLEDGE     211 

questions  of  fact  from  questions  requiring  prior  defini- 
tion, we  find  that  the  former  class  exist  on  sufferance, 
for  the  practical  purpose  of  reaching  some  sort  of  con- 
clusion in  a  reasonable  time  ;  that  in  strictness  all 
questions  either  now  are  or  are  liable  to  become  at 
any  time,  questions  of  definition  ;  and  that  even  if 
we  were  content  with  a  less  strict  view  of  the  matter, 
still  the  class  intermediate  between  questions  of  fact 
and  questions  of  definition  is  of  large  extent,  and  its 
boundaries  cannot  be  drawn  except  by  striking  a 
rough  averaij^e  of  common-sense  opinion  and  talking 
about  "  people  whom  we  need  consider."  In  this 
indefinitely  large  class  of  questions  the  need  for  the 
definition  of  their  terms  is  recognised  to  a  different 
extent  by  different  people,  and  those  who  recognise  it 
less  tend  to  regard  them  as  questions  of  fact.  So 
that  questions  of  fact,  as  a  class,  are  constituted 
rather  by  the  way  in  which  people  take  them  than 
bv  anv  quality  which  belongs  to  themselves.  Though 
1  may  obscure  the  truth  and  hinder  the  progress  of 
knowledge  by  assuming  it  to  be  a  simple  question  of 
fact  whether  ghosts  exist,  or  whether  animals  reason, 
or  whether  species  were  created,  still,  if  I  so  take  the 
question  it  is  a  question  of  fact  for  me  while  it 
remains  in  this  stagnant  condition.  To  answer  a 
complex  question  as  if  it  were  simple  is  to  end  it 
forcibly  ;  to  find  its  ambiguity  is  to  carry  on  the 
search  beyond  that  delusive  end. 

It  appears,  then,  that  although  there  are  at  all 
times  numerous  questions  which  really  deserve  to  be 
treated  as  questions  of  fact,  we  can  no  more  be  sure 
of  recognising  them  correctly  than  of  recognising 
correctly  unambiguous  terms.  To  accept  as  satis- 
factory the  distinction  between  questions  of  fact  and 


212 


USE  OF   WOIIDS  IN  UKjU^ONING       pakt  ii 


questions  of  definition  is  a  shortcoming  of  the  same 
kind  as  the  contented  acceptance  of  the  distinction 
between  uni vocal  and  e([ui vocal  terms.  In  the 
abstract  it  is  true  that  sometimes  the  doubt  whether 
S  is  1*  or  not  P  properly  turns  on  the  meaning  of  \\ 
while  at  other  times  it  properly  turns  on  the  facts 
about  S.  But  in  actual  cases  where  the  (h>ubt  has 
arisen  the  separation  of  thc.-c  two  elements  of  it  is 
often  impossible  exce|)t  at  a  serious  risk  of  misunder- 
standing the  question  and  following  irrelevant  issues. 
And  this  applies  with  greatest  force  where  the  error 
combated  is  important  without  l)ci?i^^  obvious.  The 
more  we  take  really  disputable  tjucsiious  into  arcount, 
— questions  where  the  erroneous  view  is  plausible  and 
lias  vitality,  the  more  we  find  that  to  doubt  the 
accuracy  of  the  statement  is  to  suggest  that  a  term 
which  (MH^urs  in  it  is  used  so  as  to  hide  an  important 
difference.  It  is  because  the  statement  '  Ilcrr  is  a 
sovereign  '  can  at  present  have  its  arcuracv  tested  in 
a  moment,  that  wc  call  the  •[uesLioii  a  (|Ufsiu)u  of 
fact ;  but  the  extent  of  our  agreement  with  a  religious 
or  metaphysi(;al  doctrine  is  less  easily  <listinguished 
from  the  extent  to  which  we  ret^ard  it  as  false  and 
misleading. 

Although  there  is  no  way  of  estimaLing,  even 
approximately,  the  relative  number  of  questions  whi<h 
deserve  to  be  taken  as  questions  of  meaning,  and 
although  such  an  estimate,  however  correct,  would 
have  no  bearing  upon  an  individual  case,  yet  it  may 
be  worth  while  to  notice  briefly  a  few  of  the  com- 
monest causes  which  render  questions  delusive  when 
supposed  to  be  questions  of  simple  fact.  The  cjuestion 
whether  S  '  exists '  is  perhaps  the  most  obvious  type 
of  them,  and  the  instances  quoted  just  now  will  suttice 


(;ir.  vin,  .5  49      THE  /TiOOnESS  OF  KNO  WLEDGE     213 

to  remind  us  of  many  others.  But  the  question 
whether  8  is  P  tends  also  to  l)ecome  a  question  of 
meaning  in  so  far  as  the  difficulty  of  the  decision 
}>ecomes  serious.  It  is  fairly  evident  that  a  large 
number  of  our  most  familiar  predicate  terms  refer  to 
(jualities  for  whic'h  our  tests  are  extremely  defective. 
As  we  noticed  above  (p.  207),  most  epithets  of  praise 
or  blame  are  of  this  nature  and  yet  are  widely  used 
without  much  suspicion  on  the  part  of  their  users 
that  any  <lifficulty  can  attach  to  their  interpretation. 
The  al)sence  of  such  suspicion  is  the  measure  of  our 
ignorance  of  the  way  in  which  qualities  and  defects 
are  bound  up  together,  and  the  way  in  which  hidden 
or  unconscious  motives  alter  the  character  of  an  act. 
It  is  rather  the  (diild  than  the  man,  rather  the  man 
in  the  street  than  the  man  in  the  government,  who 
call  be  inflamed  and  carried  away  by  words  that  are 
used  to  veil  or  exaf^^erate  the  facts. 

Then,  not  only  are  our  tests  defective,  but  our 
very  standards  are  often  cjuite  undetermined.  Witness 
the  wide  differences  of  opinion  we  nearly  always  get 
as  to  the  merits  of  any  book  or  play,  where  the  reader 
or  playgoer  pays  scant  regard  to  any  other  standard 
than  his  own  mood  of  the  moment.  And  even  after 
we  have  risen  to  the  conception  that  qualities  are 
to  a  jxreat  extent  relative  to  the  individual  for  whom 
they  exist  (so  that  meat  may  on  occasion  be  correctly 
described  as  poison)  there  is  another  and  more  subtle 
source  of  difficulty  in  the  fact  that  qualities,  by 
whomsoever  observed,  are  never  entirely  in  the  thing 
but  are  partly  tlie  outcome  of  its  surroundings.  If 
you  fill  up  the  valley  you  remove  the  hill ;  if  you 
deprive  a  man  of  food  or  air  he  ceases  to  be  a  man ; 
and  our  moral  character  depends  in  part  upon  our 


-•  ' 


2U 


USE  OF  WORDS  IN  REASONIXG       part  h 


income    and    other   circumstances.       *  Things  '    have 
thus  a  highly  precarious  existence.       In   this  state- 
ment, or  in  the   familiar  saying  that  circumstances 
alter  cases,  a  great  part  of  the  reason  why  (questions 
of  meaning  tend  to  appear  as  questions  of  fact  finds 
concise  expression.       Another  conception    by   which 
the   same   truth    may   he   pictured    tu   us   is   that   of 
unstable  equilibrium.       Things  as  we  know  them— 
things  as  they  are  named  and  conceived — are  balanced 
for  a  time,  and  their  fall  on  one  side  or  other  irene- 
rally  begins  before  we  are  aware  of  it.      A  little  more 
of  this  quality,  a  little  less  of  that,  and  the  balance 
is    overthrown.        Then,    often    quite    suddenly,    the 
change    is  noticeable;    A    has   ])ec()me   iion-A    by  a 
transition    which    in   its  later  stages  is   rapid.      The 
thing   called    A   has   disappeared   or   *  perished,'    and 
something  which  we  cannot   help   (tailing   non-A   is 
there    in    its   place.       Our   vision  of  these    chanjres, 
and  of  the  difficulties  they  cause  in  applying  names 
correctly,  depends  partly  on  the  state  of  our  know- 
ledge and  partly  on  the  trouble  we  choose  to  take. 
The  more  closely  we  look  at  anything,  the  more  we 
see  that  the  fusion  of  A  and  non-A  is  everywhere  to 
be  found   by   those  who  care  to  search   for   it;    for 
quality  always  implies  action  amid  surroundings,  and 
the  thing  itself  must  change  if  its  setting  changes. 
Everything  exists  only  in  a  setting  of  some  kind,  and 
its  own  character  is  partly  created  by  that  setting. 
Thus  even  our  most  durable  coins  have  an  element 
in  them  which  is  the  reverse  of  durable,  namely  their 
value  expressed   in  goods.       The   very  thing   which 
coins  exist  for  the  sake  of  measuring  is  only  measured 
by  them  in  a  questionable  way. 


cii.  vni,  j^  50      TFTE  PROGRESS  OF  KNO  W LEDGE     2 1 5 


g  50. — Thk  Virtue  and  Vice  of  Casuistry 

Having  now  seen  how  the  plausibility  of  an  inaccu- 
rate statement  depends  upon  its  unsuspected  vagueness 
and  is  destroyed  by  bringing  that  vagueness  to  light 
and   so   obtaining   further  definition,   the  next  step 
is  to  notice  that  normally  the  progress  of  knowledge 
consists  in  small  piecemeal  corrections  of  inaccurate 
statements  which  are  accurate  enough  to  be  already 
in  possession  of  the  field,  and  whose  inaccuracy  (or 
lactk   of  sufficient   definiteness)  has  hitherto  escaped 
attention.       Here  and   there,   no  doubt,   some  gross 
error  gets  corrected,  or  a  wide  new  generalisation  is 
suddenly    reached,    apparently    almost   by    accident; 
but  these  cases  are  comparatively  rare,  and  the  former 
especially  seems   likely  to  become  continually  rarer 
as  knowledge  increases.       At  any  rate  most  of  the 
work  of  adding  to  the  store  is  done  little  by  little, 
by  means  of  the  constant  interplay  between  newly- 
observed  fact  and  more  definite  theory,  or  between 
improved  theory  and  more  definite  conception  of  fact, 
— which  we  have  noticed  already  in  §  27  and  else- 
where.     To  recognise  this  is  to  recognise  the  part 
that  is  played  in  the  progress  of  knowledge  by  (what 
we    must    here    call,    for   want    of    a    better   word) 

casuistry. 

Such  recognition  is,  however,  hindered  in  many 
ways.  As  we  saw  in  last  chapter,  it  is  hindered  by 
the  confusion  between  indefiniteness  and  ambiguity, 
and  by  the  group  of  half-truths  which  support  that 
confusion  and  draw  strength  from  it.  But  a  more 
direct  obstacle  is  to  be  found  in  the  excess  of  zeal 
with   which   the  opponents  of  casuistry  have,  with 


216  USE  OF  WOIWS  IN  REASONING       partii 

the  best  intentions,  gone  about  their  work  ;  so  that 
now  the  very  name  of  the  thing  has  (3ome  to  have 
an  unpleasantly  evil  sound.  Before  it  became  thus 
degraded  it  used  to  mean  merely  the  practice  of 
testing  the  value  of  general  rules  by  applying  them 
in  particular  cases,  especially  cases  of  some  difficulty  ; 
at  present  few  people  would  take  it  in  this  impartial 
sense. 

The  opponents  consist  chiefly  of  two  parties.  On 
the  one  hand  there  is  the  paity  of  conservatism,  in- 
cluding nearly  all  varieties  oi  that  cult,  whose  best 
motive  is  to  guard  the  hard-won  treasures  of  human 
thought  against  the  spirit  that  denies  or  doubts  :  on 
the  other  hand  there  is  the  party  of  action,  whoso 
l)e8t  motive  is  to  watch  and  protest  against  the  waste 
of  time  due  to  what  they  regard  as  super -sul)tle 
inquiries.  A  third  party  might  also  possil)ly  be 
distinguished  whoso  irmor  motives  are  more  personal, 
and  who  hate  casuistry  l)ecause  it  so  often  clips  the 
wings  of  their  own  soaring  assertions.  Hut  since 
they  are  shy  of  confessing  this,  and  usually  adoi)t 
for  their  ostensible  motive  one  or  both  of  the  two 
above  mentioned,  we  need  not  here  think  of  them  as 
a  class  apart.  Indeetl,  hatred  of  o|)position  is  rather 
a  mood  tlian  a  motive, — a  mood  to  which  even  people 
of  most  irreproac-hable  motives  are  liable.  Thus  our 
quarrel  with  the  opponents  of  casuistry  does  not 
necessarily  involve  any  quarrel  with  their  motives, 
but  only  with  the  frequent  clumsiness  of  their  pro- 
cedure, with  their  frequent  lack  of  discrimination 
between  the  good  and  the  harm  of  different  sorts 
or  occasions  of  casuistry,  through  their  excess  of  zeal. 
Putting  out  of  sight,  then,  the  unfortunate  associa- 
tions that  have  gathered  round  the  word,  the  process 


CH.  VHi,  5i  50      THE  PROGRESS  OF  KNO  WLEDGE     2 1 7 

it  is  here  used  to  refer  to  is  not  quite  the  same  thing 
as  the  finding  of  ambiguities,  for  it  clovers  also  the 
unsuccessful  search  for  them.  Nor  is  it  quite  the 
same  as  experimentation,  though  that  includes  seek- 
ing as  well  as  finding ;  or  at  any  rate  the  analogy 
l)etween  casuistry  and  experimentation  is  somewhat 
disputable  or  difficult  to  see  except  where  the  ex- 
perimentation has  passed  its  earlier  stages  and  has 
plainly  for  its  object  the  greater  refinement  and 
definition  of  some  accepted  general  rule.  This  latter 
kind  of  experimentation,  however, — on  which  the 
more  gradual  improvements  of  science  mainly  depend, 
— may  serve  to  help  us  to  see  the  value  of  *  casuistry  ' 
as  well  as  the  source  of  any  harm  that  may  occasion- 
ally l>e  traced  to  it  either  in  the  shape  of  mere  waste 
of  time  or  through  the  unsettlement  of  rules  and 
principles. 

No  doubt  a  certain  amount  of  time  must  always 
be  wasted  in  the  earlier  stages  of  experimentation, — 
those  which  precede  the  putting  of  *  prudent  ques- 
tions.' But  inasmuch  as  the  less  instructed  inquiries 
pave  the  way  for  the  more  instructed  ones,  it  would 
be  a  mistake  to  count  them  as  wholly  lost  labour. 
'  Fools'  experiments,'  as  Darwin  called  them,  have  a 
value  and  interest  which  he  instinctively  recognised 
in  practice,  though  inclined  to  laugh  at  himself  for 
doing  so.^  Besides,  it  by  no  means  follows  that 
because  you  do  not  find  what  you  set  out  to  look 
for  therefore  you  find  nothing  else.  The  search  for 
general  definitions — as  contrasted  with  the  search 
for   ambiguities   and   with   the   attempt   to   get   an 

'  Soe  Life  and  Letters^  vol.  i.  p.  149.  On  p.  150  it  is  noticed  that 
"while  working  upon  the  Variations  of  Animals  and  Plants,  in  1860-61, 
he  made  out  the  fertilisation  of  Orchids,  and  thought  himself  idle  forgiving 
so  much  time  to  them." 


218 


USE  OF  WORDS  IN  REASONING       paut  ii 


ambiguity  removed — is  an  instance  in  point.  On  our 
own  principles,  it  would  seem,  to  expect  to  get  a 
satisfactory  general  definition  is  to  expect  to  catch  a 
chimera,  since  however  far  we  carry  the  pursuit  there 
is  room  for  further  inquiry.  So  there  is  ;  and  yet 
even  unsuccessful  inquiries  after  a  definition  often 
have  an  indirect  value.  It  is  not  in  the  form  of  a 
neat  verbal  result  that  the  search  for  a  general  defini- 
tion  ever  finds  its  best  justification.  Progress  is 
made,  as  a  rule,  rather  through  baffled  attempts  at 
definition.  Gradually,  as  the  problems  involved  in 
the  search  come  to  light,  we  discover  unsuspected 
ambiguities,  and  in  removing  these  we  correct  defects 
in  our  general  knowledge.  Granted,  for  instance, 
that  when  we  seek  for  a  satisfactory  general  definition 
of  *  Truth '  we  never  actually  get  it ;  still,  we  get  a 
clearer  view  than  before  of  what  is  involved  in  callintj 
an  assertion  true. 

Similarly  with  the  unsuccessful  search  for  an 
ambiguity  itself;  there  also  we  may  get  by-products. 
In  the  first  place,  so  far  as  it  is  true  that  the  dis- 
covery of  ambiguity  is  subversive  of  previous  faith, 
it  is  equally  true  that  the  result  of  an  unsuccessful 
search  for  ambiguity  is  to  estal)lish  the  faith  on  a 
firmer  foundation  than  before ;  and  in  the  second 
place,  whether  the  search  be  successful  or  not  in 
regard  to  the  particular  assertion  which  starts  the 
inquiry,  it  can  scarcely  avoid  incidentally  bringing 
to  light  ambiguities  in  other  assertions  which  are  in 
more  or  less  close  connection  with  it.  This  follows 
from  the  fact,  noticed  in  Chapter  I.,  that  we  cannot 
extend  concrete  knowledge  in  any  direction  with- 
out altering  to  some  extent  the  previous  meanings 
of  words. 


CH.  VIII,  §  50      THE  PROGRESS  OF  KNO  WLEDGE     219 

The  fairest  general  account,  however,  of  the  value 
and  harm  of  the  practice  of  searching  for  ambiguities 
is  to  be  found  when  we  consider  the  part  that  is 
played  respectively  by  ambiguity,  and  by  the  re- 
moval of  ambiguity,  in  the  progress  of  knowledge.  It 
should  be  remembered  that  though  the  critic  who 
discovers  an  ambiguity  complains  that  to  him  the 
meaning  of  the  assertion  is  non-existent,  that  is  not 
by  any  means  the  worst  of  the  harm  he  finds  in  it. 
There  is  its  effect  on  other  people  to  be  considered, — 
on  those  who  do  not  see  the  ambiguity  it  contains. 
What  it  provides  for  them  is  an  opportunity  of  shift- 
ing about  between  two  meanings,  one  safer  from 
attack  than  the  other  ;  with  the  result  that  it  hinders 
the  recognition  of  the  defects  of  a  half-truth,  and  to 
that  extent  obstructs  progress.  In  its  cruder  forms 
we  have  all  made  some  acquaintance  with  the  old 
controversial  trick  of  retiring  into  the  safer  of  two 
meanings  when  a  shifty  assertion  is  attacked,  and 
emerging  into  the  less  defensible  meaning  when  the 
attack  blows  over.  For  instance,  the  well-known  aim 
of  all  oracular  utterances  is  that  of  making  the  state- 
ment so  vague  that  its  lack  of  real  foresight  or  insight 
shall  escape  detection.  Now  the  ftict  that  we  do  not 
all  agree  in  the  way  we  distinguish  true  wisdom  from 
the  merely  oracular  imitations  of  it  should  suggest 
to  us  that  perhaps  there  is  some  real  difficulty,  on 
occasion,  in  applying  the  distinction.  And  it  is 
easy  to  see  how  the  difficulty  arises.  If  it  is  simply 
'  hedging '  which  makes  a  statement  oracular,  then 
all  generalisation  lies  a  little  open  to  the  charge. 
Generalisation,  when  expressed,  aims  at  Ijeing  literally 
true  ;  and  one  of  the  conditions  of  its  being  so  is  that 
the  letter  of  the  assertion  shall  be  just  a  little  vague. 


220 


USE  OF   WORDS  IX  1:EAS(>MXG        part  II 


The  fact  that  vagueness  is  a  necessary  con<lition  of 
all  generalisation  is  involved  in  the  fact  that  all 
general  names  are  necessarily  indefinite.  And  since 
we  are  forced  to  act  upon  approximate  knowledge  or 
else  cease  from  action  altogether  -  an  alternative 
which  no  one  can  adopt — even  statements  whitth 
suffer  a  little  from  vagueness,  and  therefore  provide 
opportunities  for  hedging,  have  a  practical  value : 
they  are  hetter  than  nothing.  Hence  it  is  that  our 
chief  expedient  for  dealing  with  difficult  matter  has 
much  in  common  with  the  {)racti<:e  of  shiftinir  alunii 
between  two  meanings.  Without  what  is  called  the 
imaginative  element  in  science,  our  knowledge  of 
Nature  could  not  have  reached  even  its  present  modest 
proportions.  The  leap  from  admitted  fact  to  unad- 
mitted is,  from  one  point  of  view,  a  shift  hetwecii 
two  meanuigs.  Our  experieiK-e  that  S  is  P  in  a  parti- 
cular case  or  set  of  cases  suggests  that  possibly  S  in 
a  wider  sense  is  P  ;  and  at  any  rate  if  we  hind  down 
*S'  to  mean  just  the  cases  observed  and  no  others, 
we  cannot  make  a  single  step  forward  in  generalising. 
But  we  never  do  so  bind  it  down  ;  we  leave  the 
margin  of  its  application  a  little  vague  on  purpose, 
and  cast  about  for  further  hints  to  iruide  us  in  e\- 
tending  it,  or  to  check  our  first  inclination  to  extend 
it  too  widely. 

Since,  then,  vagueness  in  itself  is  occasionally  a 
virtue,  we  cannot  condemn  oracularity  so  long  as 
we  mean  l)y  it  simply  vagueness  of  statement.  The 
intellectual  sin,  the  controversial  weakness,  lies  not 
in  the  mere  shift  between  two  meanings,  but  in  the 
spirit  in  which  it  is  made  and  in  the  conseipient 
attitude  towards  criticism.  To  play  the  oracle  is  to 
make  a  pretence  of  knowledge,  not  merely  to  have 


CH.  vni,  5<  50      THE  PROCIIESS  OF  KXO  WLELGE     221 

faith  where  vision  is  dim.  And  though  in  the  subtler 
cases  it  may  sometimes  l)e  difficult  to  distinguish 
between  ftiith  and  make-believe,  and  between  make- 
i>elieve  and  sham,  at  any  rate  there  are  thousands 
of  everyday  matters  where  the  difficulty  is  almost 
non-existent.  As  a  simple  instance  we  may  take  the 
ditierence  between  the  old  weather  almanacs,  which 
used  to  predict  for  a  year  ahead,  and  the  modern 
weather  forecasts  in  the  daily  papers.  The  latter 
predictions  are,  indeed,  a  little  less  vague  than  the 
former,  but  even  they  depend  for  their  success  to 
some  extent  upon  their  vagueness.  The  whole  country 
is  divided  into  a  few  sections  of  considerable  size,  and 
a  forecast — itself  often  somewhat  vaguely  worded — 
given  for  the  whole  of  each  section.  Areas  much 
smaller  than  these  would  leave  room  for  the  forecast 
to  be  both  riglit  and  wrong  at  once.  But  the  real 
difference  lies  in  the  attitude  taken  by  the  two  differ- 
ent sets  of  prophets.  The  one  set  lived  by  concealing 
their  ignorance  and  evading  criticism  ;  the  other  set 
freely  ndnnt  their  ignorance  and  look  to  criticism  as 
the  best  means  of  reachincr  i'uller  knowled<^e. 

Secondly,  just  as  the  practice  of  shifting  between 
two  meanings  is  false  or  truthful  according  to  the 
motive  which  underlies  it,  so  the  critical  inquiry 
itself  is  capable  of  becoming,  according  to  its  motive, 
either  a  valual)le  aid  in  the  search  for  truth  or  a 
weak  and  silly  obstruction.  The  practice  of  fishing 
for  possible  ambiguities  can  no  more  be  in  itself  con- 
demned than  the  plan  of  leaving  a  margin  of  vao-ue- 
ness  for  the  sake  of  getting  a  working  belief.  Each 
method  is  needed  if  knowledge  is  to  grow.  Just 
as  no  generalisation  can  be  formed  without  going 
through  stages  of  incompleteness,   so  no  ambiguity 


I 


M 


222 


USE  OF  WORDS  IN  REASONING       part  ii 


can  be  clearly  seen  without  having  first  been  vaguely 
suspected.  In  the  one  case  as  in  the  other,  all  de- 
pends on  the  honesty  of  the  motive  and  on  readiness 
to  admit  the  tentative  nature  of  what  is  l)eing  done. 
The  tentative  process  need  not  involve  any  pretence, 
and  it  is  only  pretence  that  makes  a  quibble  of  eitlier 
opposite  kind. 

On   the   whole,  then,   we   seem   driven   to  admit 
that  the  question  whether  casuistry  is  a  virtue  or  a 
vice  is  one  of  those  over-wide  questions  which    do 
not    allow  of  a   simple    answer.      The    only    fruitful 
question    is    whether    in    the    particuhir   instance    of 
its  application  it  can  be  justified  or  not.     But  it  is 
at  any  rate  a  gain  if  we  have  clearly  seen  the  folly 
of  any  general  condemnation  of  the  practice  of  facing 
possible  exceptions  to  a  rule.     The  war  between  the 
adherents   of  simple  rules   and    those   interested   in 
exceptions    is    not    waged    only    on     those    fields   of 
thought  where    there    is    much  to    be    said   for  the 
bliss  of  ignorance.     The  difficulty  is  of  greatly  wider 
range,    and    notoriously    there     are    generalisations 
which  do  not  deserve  any  reverential  treatment.     No 
one,   we  may  presume,   would  carry  his  dislike   for 
casuistry  so  far    as   to  condemn  all  criticism  of  the 
loose   rules  which  are   often    made  about   classes  of 
people,  such  as  negroes,  or  minor  poets,  or  foreigners, 
or  the  upper  or  lower  classes  of  society.     Every  one 
knows  that  such  rules  often   have  a  orreat  deal   of 
truth  in  them,  and  yet  nearly  every  one  (when  in  a 
reasonable  mood)  recognises  that  they  can  be  believed 
too   rigidly.      And   between   the  two  extremes — be- 
tween  the   rules  which   it  is  better  not  to  criticise 
carefully  and  those  which  are  obviously  defective — 
there  is  the  largest  class  of  all,  the  half-truths  which 


CH.  VIII,  5^  5 1      THE  PROGRESS  OF  KNO  W LEDGE     223 

are  nearly  true  and  yet  will  l)ear  improving.  As 
moral  casuistry  may  be  a  symptom  of  the  need  of  a 
moral  tonic,  so  the  lack  of  casuistry  in  other  subjects 
may  be  a  symptom  of  the  commonest  intellectual  vice. 
At  any  rate  it  is  mainly  through  recognising  the 
complex  relation  between  theory  and  fact,  or  rules 
and  exceptions,  that  we  can  best  understand  the 
growth  of  knowledge,  especially  as  regards  the  diffi- 
culties under  which  it  labours  and  the  hope  that  for 
ever  leads  men  forward  in  spite  of  constant  partial 
failure. 

8  51. — The  Function  of  Scepticism 

From  the  two  preceding  sections  we  may  draw 
some  consequences  which  have  a  bearing  upon  that 
old  issue,  the  place  and  function  of  Scepticism  in 
philosophy. 

The  name  scepticism,  like  casuistry,  is  one  of  the 
many  words  which  have  degenerated  through  the 
influence  of  their  traditional  denotation  ;  so  that  to 
say  anything  in  favour  of  scepticism  is  sure  to  lay 
one  open  to  the  attacks  of  those  who  mean  by  it 
iiotlung  more  than  a  special  form  of  dogmatic  meta- 
physics  which  has  long  been  discredited  and  which 
It  is  unlikely  that  any  one  now  upholds.  Probably 
there  is  no  living  philosopher  who  ever  overlooks 
the  fact  that  in  so  far  as  we  claim  to  know  anything 
—even  to  know  the  impossibility  of  this  or  that  kind 
of  knowledge— our  scepticism  falls  short  of  com- 
pleteness. Nor,  we  may  equally  assume,  is  there 
any  philosopher  who  does  not  know  that  denial  (i.e, 
mtelligent  denial)  rests  on  and  requires  something 
taken  as  known.  To  deny  without  reasons  for 
denying  would  of  course  be   to   deny   in   language 


224 


USE  OF  WORDS  IN  REASONING       part  ii 


only,  not  in  thought,  though  to  deny  intelligently 
and  yet  without  suJftcirtU  reasons  lor  denying  in 
notoriously  possible. 

Is  doubt,  like  denial,  thus  indirectly  assertive  ? 
Intelligent  doubt,  or  reservation  of  judgment,  difl'ers 
at  any  rate  from  intelligent  denial  in  one  respect, 
— that  it  does  not  necessarily  presuppose  a  know- 
ledge of  what  the  assertion  is  that  you  are  asked  to 
accept.  You  cannot  deny  intelligently  without 
knowing  what  it  is  that  you  are  denying,  but  you 
can  intelligently  reserve  judgment  when  confronted 
with  a  statement  which  you  find  to  be  ambiguous. 
Or  rather,  that  is  the  only  intelligent  attitude  in  such 
cases ;  to  accept  or  deny  or  dispute  the  statement, 
as  if  it  really  conveyed  an  assertion,  would  l)e  to 
show  a  lack  of  intellit^ence. 

These  elementary  truths  seem  perhaps  hardly  to 
need  stating.  Yet  there  are  still  some  philosophers 
who  can  at  any  rate  appear  to  forget  them  when 
the  juggle  l)etween  doubting  intelligently  in  the  one 
sense  and  doubting  intelligently  in  the  other  is 
needed  to  support  a  weak  case.  When  you  have 
pointed  out  that  some  statement  of  theirs  is  am- 
biguous, and  therefore  (till  the  ambiguity  is  removed) 
non-assertive,  they  pretend  that  you  can  only  have 
disputed  its  truth,  and  not  its  assertive  force.  They 
would  hardly,  perhaps,  go  so  far  as  to  say  in  so 
many  words '  that  there  is  no  such  thing  as  the  latter 

*  At  times  they  come  rather  near  this.  See,  for  instance,  Mr.  Bradley's 
Apf)eariim:e  and  lieality,  2nd  edition,  p.  559,  He  has  indeed  managed  to 
obscure  liis  argument  by  giving  also  a  plainly  imjMJssible  account  of  his 
op{>onents'  views, — an  account  the  character  of  which  is  further  suggested  by 
the  remarkable  abseme  of  any  attemjtt  to  sup|>ort  it  by  quotations.  How- 
ever, the  sober  and  relevant  i»art  of  his  contention  may  be  found  if  wf 
neglect  this  false  issue  and  all  that  belongs  to  it.  There  remain  the  two 
statements  that  "to  (juestion  or  doubt  intelligently  you  must  understand,  " 
and  that  ' '  if  about  any  theory  you  desire  to  ask  intelligently  the  question 


CH.  vui,  S  5 1       THE  PROGRESS  OF  KNO  WLEDGE     225 

kind  of  doubt,  but  they  do  their  utmost  to  put  it 
out  of  court,  and  they  speak  as  if  the  former  kind 
alone  were  possible, — the  kind  that  (like  denial) 
comes  into  operation  only  after  the  ambiguity,  if 
any,  has  been  removed.  Thus  the  dilemma  into 
which  they  try  to  put  their  critics  is  the  familiar 
one  of  **  Heads,  I  win ;  tails,  you  lose  "  ;  for  if  you 
attack  their  statement  without  observinor  its  am- 
biguity  they  can  always  meet  your  objections  from 
the  safest  of  cover ;  while,  if  you  ask  them  to  choose 
between  its  possible  meanings  and  to  abide  by  the 
choice,  then  they  claim  that  you  have  yourself  con- 
fessed that  you  do  not  understand  the  assertion,  and 
therefore  that  your  doubt  is  '  unintelligent.'  This 
attitude  towards  criticism  reminds  one  a  little  of  the 
Boers'  reported  complaint  at  Poplars  Grove,  that 
it  was  not  fair  to  turn  their  positions  instead  of 
delivering  a  frontal  attack, — that  it  was  not  playing 
the  game.  After  all,  the  business  of  the  attacking 
party  is  not  to  walk  into  traps,  but  rather  to  avoid 
them.  Still,  it  was  of  course  annoying  for  the  Boers, 
after  having  dug  their  trenches  with  so  much  labour 
and  education.  No  wonder  they  fumed  as  they  ran 
away. 

But  we  are  not  here  specially  concerned  with  the 
humours  of  controversy.  Our  question  is,  rather,  as 
to  the  nature  of  the  scepticism  which  declines  to 
stultify  itself  by  claiming  to  know  more  than  it  does 

'  What  does  it  mean  ? '  you  must  be  prepared  to  enter  into  that  theory."  The 
second  of  these  statements  seems  to  admit  (what  the  first  expressly  denies) 
that  there  can  be  intelligent  inquiry  for  a  meaning;  but  the  admission  is 
deceptive,  since  we  are  left  asking  how  the  required  prej)aration  is  to  be 
obtained  in  cases  where  you  have  found  the  theory  ambiguous.  If  by  *  pre- 
l>ared  '  he  merely  means  'willing'  then  he  imi)lies  that  the  request  for  the 
removal  cf  an  lunbiguity  can  never  be  seriously  meant.  But  I  presume 
^Ir.  Bradley  knows  better  than  that. 

15 


22G 


USE  OF  ]nu:/)S  IX  JIEASuXIXG        pautu 


\  \ 


: 


know  a1)0iit  the  limits  of  knowledge.  Of  course  it  is 
open  to  any  one  to  say  that  a  scepticism  wliich  is 
wary  enough  to  do  this  is  not  the  real  thing,  and  does 
not  deserve  the  name, — that,  in  sliort,  no  scepticism 
is  genuine  unless  it  departs  from  its  own  original  idea 
and  becomes  dogmatic.  In  the  same  way  it  might  i)e 
argued  that  history  is  not  history  unless  it  is  biassed 
and  therefore  largely  false.  These  are  matters  for 
those  who  care  about  them  to  settle  for  themselves. 
On  the  princii)les  here  throughout  admitted  it  is  clear 
that  the  ((uestion  what  name  siiall  be  given  to  om- 
particular  'ism'  cannot  be  taken  as  of  chief  import- 
ance ;  far  be  it  from  us  to  insist  on  this  or  that  label 
or  banner  so  loni;  as  the  views  themselves  are  under- 
stoo<l.  What  wo  cannot  accept  is  the  argument  that 
a  stated  doctrine  stands  above  the  reach  of  any  <loubts 
because  its  assertor  chooses  to  ignore  all  doubts 
except  those  which  he  can  safely  answer.  We  cannot 
allow  him,  without  a  protest,  to  hold  the  too  con- 
venient position  that,  if  we  are  to  criticise  his 
doctrine  at  all,  we  must  do  so  by  putting  out  of  sight 
our  only  real  objection.  If  the  defendant  could 
always  dictate  to  the  complainant  the  way  in  which 
the  hitter's  case  should  be  conducted,  what  a  comfort- 
able time  there  would  be  for  defendants  jjenerallv. 

Whatever  name,  then,  may  be  thought  most 
suitable  to  the  position  we  have  here  reached  as 
re^ijards  the  trustworthiness  of  human  knowledge,  the 
position  itself  may  be  provisionally  described  as 
follows  : — 

First,  we  see  no  reason  for  allowing  that  purely 
abstract  truths — of  which  *  A  is  A  '  may  be  taken  as 
the  type — are  judgments ;  they  represent,  rather,  the 
prior  conditions  of  judgment  ;    in   themselves    they 


cif.  vnr,  §  51      THE  PROGRESS  OF  KXOWLEDGE     227 

involve  no  choice  between  yes  and  no,  and  a  mind 
from  which  they  are  absent  would  be  wholly  incapable 
of  thought. 

Secondly,  judgments,  we  have  seen,  may  always  be 
analysed  into  a  part  which  is  admittedly  theoretical 
and  a  part  which  is  taken  (with  certain  reservations) 
as  fact.     And  the  closer  we  look  at  either  of  these 
elements  of  a  judgment  the  less  can  we  feel  convinced 
that  they  are  final  decisions,  or  safe  against  future 
correction  and  improvement.     As  the  past  history  of 
human  judgment  shows,  our  theories  are  constantly 
turning  out  to  be  more  vaguely  apprehended  than  we 
had  hitherto  supposed,— are  constantly  found  to  be 
statements  of  rules  with  an    insufficient    regard  for 
their  exceptions ;  and  our  '  fticts '  at  the  same  time 
are  found  to  be  loaded  with  unsuspected  theory.     But 
we  can  also  see  reasons  for  expecting  this  process  to 
continue  far  into  the  future.     Over  and  above  the 
defects  of  our  knowledge  which  are  due  to  the  mere 
ImiiLations  of  our  senses,  and  to  our  other  physical 
disabilities  such  as  that  of  being  in   two  places  at 
once,  the  very  instrument  by  which  all  our  reflective 
thought  is  carried  on  is  itself  essentially  a  source  of 
t^Tor ;  l)oth  our  theories  and  our  facts  are  liable  to 
the  defects  which  are  inherent  in  language.     Descrip- 
tive words  must  l)e  employed  whether  in  stating  or 
conceiving  our  theories  and  facts;    and  descriptive 
words,  as  we  have  seen,  are  never  fully  descriptive, 
and  thus  leave  room  for  ambiguity  and  consequent 
plausil)le  error.     The  theory  that  from  M  follows  P 
has  to  be  connected  with  the  '  fact '  that  S  is  M,  in 
such  a  way  as  to  rule  out  the  objection  that  M  in  the 
two  premisses  does  not  mean  quite  the  same  thing. 
Until  words  can  be  freed  from  their  vice  of  indefinite- 


228 


USE  OF  WORDS  IX  llEASONIXG       I'akt  ii 


ness — and  no  one  at  present  has  the  remotest  concep- 
tion how  this  can  be  done — the  end  of  the  process 
of  improving  our  judgments  is  merely  wherever  we 
choose  to  make  an  end  of  it  for  the  time. 

In  practice  the  greatest  difficulties  are  encountered 
when  it  is  not  clear  which  of  the  two  elements  in  the 
judgment  (fact  or  theory)  is  most  in  need  of  correc- 
tion ;  but  since  all  correction  must  have  a  definite 
point  of  attack,  we  can  m  these  cases  only  consider 
each  element  in  turn.  And  in  both  alike  the  procedure 
is  the  same.  The  theory  that  from  M  follows  P  is 
attacked  by  the  suggestion  of  exceptional  cases  which 
show  the  need  of  further  defining  M,  so  as  to  state 
the  rule  less  vaguely.  The  supposition  that  the 
predicate  M  is  rightly  applied  to  S  involves  the 
theory  that  the  difference  between  S  and  the  less 
doubtful  members  of  the  class  M  has  no  importance 
for  the  purpose  immediately  in  hand  ;  and  a  discussion 
of  this  theory  involves  an  answer  to  the  question  how 
the  class  M  shall  be  sufficiently  defined. 

On  the  whole,  then,  it  appears  that  the  weak  point 
in  human  certainty  is  the  need  of  expressing  our 
judgments  in  language,  or  of  tacitly  conceiving  them 
as  if  they  were  expressed  in  language.  For  on  the 
one  hand  we  cannot  shake  off  our  inveterate  but 
vague  assumption  that  the  *  Laws  of  Thought '  are 
somehow  true,  and  on  the  other  hand  we  cannot 
apply  them  to  actual  words  used  without  making  the 
untenable  assumption  that  ambiguity  is  impossible, — 
untenable  because,  as  we  have  seen,  it  lies  in  the 
nature  of  language  that  descriptive  words  shall,  as 
such,  be  liable  to  cause  ambiguity.  That  is  the  least 
assailable  ground  of  the  sceptical  difficulty  that  exists 
at  the  present  time, — the  difficulty  which  the  older 


CH.  vni,  §  5 1      THE  PROGRESS  OF  KNO  W LEDGE     229 

sceptics  may  have  felt  but  which  they  did  not  clearly 
recognise. 

Thus  when  it  is  asked  whether  we  know  Reality, 
the  only  possible  answer  seems  to  be  that  we  do  not 
know  how  much  or  how  little  we  know^  it.  What  we 
do  know — subject,  of  course,  to  future  correction — is 
that  our  judgments  always  contain  the  seed  of  possible 
error.  Along  with  the  unknown  amount  of  truth 
they  contain  goes  an  equally  unknown  amount  of 
correct ibility,  and  the  whole  history  of  human  thought 
is  a  history  of  the  partial  correction — or  at  least 
supposed  partial  correction — of  previous  errors.  Only 
in  this  way  and  to  this  extent  are  we  driven  to 
recognise  a  difference  between  Reality  as  it  is  and 
Reality  as  it  is  thought, — only  so  far  as  the  refusal 
to  recognise  it  would  amount  to  the  doctrine  that 
there  is  no  such  thing  as  error  so  long  as  self- 
contradiction  is  avoided ;  or  that  human  knowledge, 
when  self-consistent,  is  not  (to  an  unknown  extent)  in 
constant  need  of  partial  correction. 

Is  this  position  *  dogmatic '  ?  Only  if  all  reasoned 
belief  is  dogmatic,  even  when  w^e  are  fully  prepared  to 
reconsider  it  for  further  reason  shown.  The  mere  name 
*  dogmatic '  need  not  frighten  us,  if  it  be  meant  to 
spread  so  wide  a  net  as  this.  Our  view  of  the  nature 
of  language,  and  of  its  connection  with  thought,  is  at 
any  rate  not  put  forward  otherwise  than  as  a  challenge 
to  objectors  to  find  definite  fault  w4th  it.  Our  positive 
basis  claims  to  be  no  more  than  a  web  of  theories,  and 
to  hold  good  only  until  it  shall  be  superseded  by 
improved  theories  of  the  same  improvable  kind.  That 
is  to  say,  it  puts  forward — not  as  a  piece  of  absolute 
truth  which  all  men  must  accept  or  be  damned,  but  as 
a  theory  openly  rested  on  reasons  which  challenge  the 


230 


USE  OF  WOllDS  IX  llEASOXiya       TAin  II 


fullest  criticism — the  assertion  that  human  knowlech'e 
IS  progressive,  and  therefore  imperfect  and  liable  to  an 
unknown  amount  of  correction.  Imperfect  knowledcre, 
as  Mr.  Bosanquet  says/  only  becomes  false  when  mis- 
taken for  perfect  knowledge;  and  the  function  of 
scepticism  is  precisely  to  prevent  this  mistake  so  fiir 
as  it  can.  As  to  the  question  whether  the  imperfection 
is  eternal  or  not,  our  position  is  that,  as  far  as  we  at 
present  see,  it  is  so,  or  that  an  end  to  the  process  of 
gaining  further  knowledge  is  no  more  conceivable  (by 
us  at  present)  than  an  end  to  Space  or  Time.  Since 
these  views  themselves  lie  open  to  correction,  their 
statement  is  only  a  request  to  let  the  detailed  correction 
begin. 

It  is  in  this  way,  then,  that  we  disarm  the  wordy 
arguments  which  seek  to  prevent  scepticism  from 
having  a  standing -ground.  Under  whatever  form 
they  appear,  in  the  end  they  all  amount  to  the  doctrine 
that  sceptism  must  contradict  itself  and  become  do*'-- 
matic  ;  but  where  is  the  contradiction  in  admittinf^ 
that  we  may  be  mistaken  in  regard  to  any  piece  of 
theory — even,  for  instance,  in  this  piece  of  theory 
itself  {  Granting  that  the  assertion  ''  I  am  sure 
that  I  am  everywhere  fallil)le"  contradicts  itself, 
how  can  the  same  objection  be  brought  against  a  mere 
request  on  the  part  of  the  sceptic  to  hear  what  definite 
fault  can  t)e  found  with  the  reasoned  theory  that 
human  knowledge  is  progressive  and  therefore  im- 
perfect, or  with  the  other  reasoned  theories — as  to 
the  part  played  by  language  in  judgment,  or  as  to  the 
inevitable  defect  of  language — on  which  our  view  of 
man's  fallibility  is  grounded,  and  by  which  its  very 
meaning  is  explained?      Assertion   in    itself  is   not 

'   Log'w,  i.  '1'2Z. 


n\.  VIII,  i5  51      THE  PROGRESS  OF  KXO  WLEDGE     231 

dogmatic,  but  only  l)ecomes  so  when  we  seek  to  evade 
art^unients  brou^jht  ac^ainst  it.  To  confuse  assertion 
with  dogmatic  assertion  is  to  go  l)ack  to  over-simple 
notions  of  the  nature  of  Truth.  When  we  recognise 
that  all  truth  as  stated  contains  an  unknown  amount 
of  error,  we  cannot  easily  be  dogmatic  in  any  sense 
that  carries  l)lame. 

Among  the  consequences  of  this  general  position, 
two  may  l)e  mentioned  as  having  a  special  interest  for 
Loo^ic.  First,  the  clumsy  abstract  distinction,  with 
which  we  all  start,  between  good  and  bad  reasoning, 
or  !»etween  'logical  proof  and  the  absence  of  logical 
proof,  cannot  be  maintained  except  as  a  mere  figure  of 
s})ecch,  like  '  perfectly  definite '  or  '  completely  descrip- 
tive.' In  its  place  we  have  the  distinction  between 
sutHcient  and  insufficient  proof,  with  an  implied  refer- 
ence to  some  purpose  for  which  the  proof  in  question 
does  or  does  not  sufiice.  It  is  only  in  this  w^ay  that  we 
can  accept  and  yet  render  harmless  the  theory  that  all 
known  truth  is  progressive  and  liable  to  alteration, 
and  that  therefore  absolutely  certain  proof  of  any 
assertion  is  a  thing  unknown.  All  proof  is  bad  in 
this  sense  and  to  this  extent ;  and  accordingly  if  we 
are  to  make  any  distinction  at  all  between  good  and 
bad  proof  it  must  be  on  some  less  exalted  level 
than  the  hope  of  reaching  absolute  certainty.  It  is 
not  possible  indeed  to  set  up  any  general  standard 
to  correspond  to  what  are  commonly  and  vaguely 
referred  to  as  '  practical  purposes,'  for  the  simple 
reason  that  the  practical  purposes  for  which  proof  is 
required  are  extremely  various.  For  instance,  life 
and  death  at  times  depend  on  correctness  of  judgment, 
while  at  other  times  our  desire  for  accuracy  dwindles 
away  to  nothing.     Proof  '  for  practical  purposes '  thus 


232 


USE  OF  WORDS  IN  REASONING       part  ii 


covers  every  variety  of  standard  used.  We  need  not, 
however,  make  more  of  this  difficulty  than  it  deserves. 
All  that  is  required,  in  any  particular  discussion,  is  an 
agreement  as  to  the  purpose  for  which  the  proof  is 
to  be  sufficient,  and  though  this  may  of  course  be 
difficult  to  get  with  precision,  a  roughly  approximate 
agreement  will  at  any  rate  serve  for  a  l)eginning,  and 
you  can  hardly  avoid  making  either  the  agreement  or 
the  difference  of  standard  more  precise  as  the  dis- 
cussion proceeds.  In  one  respect  it  does  not  much 
matter  which  of  these  results  occurs.  For  when  an 
assertor  can  only  defend  his  position  on  the  ground 

that  the  tests  you  are  applying  are  too  severe,  then 

always  supposing  you  are  aiming  at  something  short 
of  an  impossibly  absolute  certainty— your  difference 
of  standard  is  not  very  important,  because  it  causes 
no  confusion.  The  two  parties  are  then  in  the  position 
of  those  who  agree  to  differ ;  that  is  to  say,  each  may 
admit  the  other  to  be  right,  *  from  his  own  point  of 
view,'  while  preferring  another  point  of  view  for  him- 
self. Meanwhile,  even  with  so  little  result  as  this, 
some  new  light  is  usually  thrown  on  the  truth  of  the 
matter  disputed.  A  discussion  which  ends  in  an 
agreement  to  differ  is  a  very  different  thing  from  a 
discussion  which  ends  in  a  deadlock.' 

Secondly,  the  view  that  in  all  judgment  there  is 
room  for  the  misconception  of  fact  involves  the 
admission  that  any  correction  to  be  made  in  a  judg- 
ment can  be  only  partial.  Just  as  there  cannot  be 
statements  of  fact  which  are  necessarily  true,  so  there 
can  be  no  belief  which  is  completely  false.  Since  a 
false  fact  is  a  true  fact  misconceived,  there  is  always 

*  A  deadlock  arises  only  wliere  rith.r  |»aity  pui>  an  ond  lo  the  tlisi  ussion 
against  the  desire  of  the  other,  whatever  his  motive  inav  Vk'. 


CH.  vni,  §  5 1      THE  PROGRESS  OF  KNO  WLEDGE     2  3  3 

a  basis  of  truth  in  the  falsest  possible  fact.  That  is  in- 
deed one  reason  why  (as  we  saw  at  p.  127)  it  is  useless 
in  argument — except  on  the  rare  occasions  when  strong 
language  is  really  strong — to  declare  that  a  statement 
is  *  wholly  false ' ;  the  more  effective  thing  to  do 
is  to  get  as  near  as  possible  to  the  point  at  which  the 
misconception  crept  in  ;  to  see  the  error  being  added, 
by  mistake  or  misrepresentation,  to  the  true  fact  that 
underlies  it.  Only  so  far  as  this  can  be  done  is  the 
error  explained,  or  its  nature  clearly  seen.  No  refuta- 
tion can  be  crushing  or  convincing  so  long  as  it  fails 
to  give  some  hint  as  to  what  the  error  consists  of, — i.e. 
where  it  departs  from  the  truth. 

Our  scepticism,  it  will  now  be  seen,  consists  of  a 
recognition  of  the  defects  of  knowledge  only  in  the 
hope  of  helping  knowledge  forward.  Among  its  lead- 
ing principles  are  these  : — that  doubt  is  always  lawful 
but  not  always  expedient' ;  that  human  fallibility  is 
only  worth  remembering  for  the  sake  of  discovering 
and  correcting  actual  errors ;  and  that  beliefs  may  be 
unquestioned  without  being  unquestionable.  So  far 
from  using  the  notion  that  man  is  fallible  as  an  excuse 
for  despair,  or  for  tendering  the  advice  that  nothing 
should  ever  be  believed,  we  use  it  as  a  justification  of 
the  effort  to  improve  our  knowledge  little  by  little  for 
ever. 

And  such  being  the  nature  of  this  kind  of  scepti- 
cism, it  follows  that  the  determination  to  feel  our  way 
towards  truth  by  discarding  all  visible  error  neces- 
sarily employs  the  method  of  casuistry  at  every  step ; 
necessarily  therefore  resolves  itself  into  a  search  for 

^  We  should  also  admit  that  doubts  are  not  only  not  always  expedient 
but  are  not  always  even  possible.  That  is  to  say,  a  given  person  at  a  given 
time  may  find  a  given  doubt  beyond  his  j»ower  ;  and  for  no  human  being  is 
anything  like  consistent  universal  doubt  a  i)08sibility. 


234 


USE  OF  WOIWS  IX  REASONING       part  ii 


latent  ambiguities,  a  search  which  is  successful  in 
aiding  the  progress  of  knowledge  in  so  far  as  it  brings 
actual  ambiguities  to  light.  Thus  the  interest  in 
finding  ambiguities  is  not  controversial  merely,  but 
is  co-extensive  with  the  need  for  distinguishing  within 
a  class  two  portions  which  for  some  clearly-seen  pur- 
pose are  essentially  different.  And  this  movement 
of  thought  towards  clearer  definition  is  at  once  the 
effect  and  the  cause  of  every  step  in  the  progress  of 
knowlediie. 


I  have  roiul  with  interest  Prof.  Watson's  criticism  on  my 
supjxjsed  position,  in  his  Onfline  of  Philosophj/^  pp.  329-336. 
Wliile  it  shows  that  some  of  my  former  expiessions  were  open 
to  genuine  misinterpretation,  it  allows  me  to  think  that  the 
statement  just  given  will  suthee  to  explain  them.  If  not,  I  shall 
be  happy  to  continue  the  discussion  at  any  time.  The  following 
additional  points,  however,  may  be  noticed  at  once : — 

(1)  The  complaint  (p.  332)  about  my  use  of  the  word  'per- 
ha[)s'  originates  in  Prof.  Watson's  having  taken  it  out  of  one 
sentence  and  put  it  in  another.  But  this  I  assume  to  have  been 
a  mere  slip,  and  there  is  no  need  to  make  much  of  it.  A  rciil 
ditiiculty  is  to  know  how  to  please  a  critic  who,  when  I  leave 
out  the  word  '  perhaps,'  complains  of  my  dogmatic  confidence, 
and  when  I  am  su{)posed  to  put  it  in  complains  of  my  excessive 
caution.  The  truth  is  that  none  of  my  assertions  are  put  forward 
except  as  liable  to  the  risk  of  error,  and  as  asking  to  have  the 
error  shown.  But  would  not  readers  have  a  just  cause  of  offence 
if  a  writer  were  to  repeat  this  disclaimer  expressly  in  every 
sepai-ate  sentence  1  This  is  chieHy  a  (juestion  of  style  and  literary 
manners.  We  cannot  in  the  name  of  philosophy  decide  the 
question  whether  a  given  assertion  is  dogmatic  or  not  merely  by 
the  absence  or  presence  of  verbal  expressions  of  doubt  in  the 
sentence, — expressions  which  the  writer  takes  to  be  needed,  or 
to  be  superfluous,  on  literary  grounds  alone.  The  dogmatic 
quality  of  assertion,  I  submit,  can  depend  on  nothing  but  the 
assertor's  attitude  towards  criticism. 

(2)  In  the  passiige  cited,  I  did  not  call  the  Laws  of  Tliought 


<'H.  vin,  .^  51      TEE  PnO(7RESS  OF  KNO  WLEDGE     235 

•  anthropomorphic,'— a  description  of  them  which  would  seem 
to  me  nonsensical ;  the  name  was  attached,  rightly  or  wrongly, 
to  a  certain  conception  of  Reality.  And  unless  Prof.  Watton 
would  maintain  that  it  is  impossible  for  a  human  being  to  have 
any  excessively  anthropomorphic  conceptions,  his  argument  seems 
to  lead  nowhere. 

(3)  Prof.  Watson  is,  1  think,  scarcely  just  towards  Mr. 
Bradley  in  saying  (j).  334)  that  he  meant  no  more  by  claiming 
'  unconditional  knowledge  of  Reality  '  than  to  affirm  that  '  Reality 
is  absolutely  complete.'  If,  however,  this  were  so,  my  objections 
against  the  truistic  futility  of  Mr.  Bradley's  main  positive  result 
would  be  all  the  stronurer. 

(4)  "  It  may  well  be  that  Scepticism  .  .  .  has  a  deeper  mean- 
ing when  it  is  viewed  merely  as  a  sUige  in  the  process  hy  wliich 
higher  truth  is  reached."  But  that  is  exactly  how  I  have  always 
viewed  it ;  and  that  conception  of  it  is  one  reason  \y\\y  \  would 
avoid  identifying  '  Scepticism  '  with  those  so-called  sceptical  posi- 
tions only  which  do  not  admit  of  useful  employment.  The  last 
paragraph  in  Prof.  Watson's  criticism  makes  me  wonder  whether, 
apart  from  disguises  of  ])anner  and  shibboleth,  his  view  and  mine 
are  really  as  divergent  as  a  healthy  party  spirit  might  desire. 
So  long  as  we  both  recognise  that  '  Reality  as  it  is  thought '  need 
not  be  the  same  as  '  lieality  thought  correctly,'  there  is  still  some 
work  left  for  science  and  philosophy  to  do. 


PART  III 


THE   LEADING  TECHNICALITIES  OF 

FORMAL   LOGIC 


CHAPTER   IX 

kinds  of  name  or  term 

8  52. — '  Logical  Character  ' 

We  have  now  to  observe  in  some  detail  how  the 
leading  assumptions  ^  of  Formal  Logic  introduce  con- 
fusion into  the  technical  terminology  and  render  it 
useless  for  expressing  logical  doctrines  with  precision. 
It  will  not  be  possible  to  deal  with  these  assumptions 
in  perfect  independence  of  each  other,  since  they  are 
only  diflerent  aspects  of  the  same  tendency  to  pay 
excessive  attention  to  form,  and  it  sometimes  happens 
that  one  of  them  aids  and  abets  another.  But  a 
rough  separation  of  them  may  be  made  if  we  follow 
the  usual  three-fold  division  which  the  textbooks 
adopt  in  their  account  of  the  technicalities, — the 
account  given  of  terms,  of  propositions,  and  of  argu- 
ments. The  form  of  a  word,  or  of  an  assertion,  or  of 
an  argument,  is  too  easily  accepted  as  determining 
its  '  logical  character.' 

Formal   Logic,  as  Dr.   Keynes  openly  says,^  *  has 

^  Three  of  these  were  mentioned  in  Chapter  1.  : — 

(1)  That  the  •  logical  character  '  of  a  word,  or  of  an  assertion,  belongs 

to  it  (juite  independently  of  its  context ; 

(2)  That  sentence  and  assertion  are  the  same  thing  ; 

(3)  That  the  reasoning  process  is  distinct  from  its  subject-matter. 

2  Formal  Ijxjic,  3rd  ed.  p.  3.     Among  the  passages  where  this  principle 
is  departed  from,  I  note  the  following  in  his  first  chapter :— At  p.  7  Dr. 


240 


USE  OF  WORDS  IN  REASONING      part  hi 


no  cognisance '  of  context,  and  though  in  a  few  in- 
stances his  book  does  take  cognisance  of  it,  yet  it 
clearly  does  so  against  its  own  express  intention  and 
to  a  very  limited  extent.  This  neglect  of  context  is 
chiefly,  though  not  exclusively,  shown  in  the  distinc- 
tions drawn  among  kinds  of  '  terms '  or  names.  The 
more  expressly  formal  any  Logic  is,  the  more  openly 
is  the  assumption  made  that,  when  a  list  of  names  or 
of  sentences  is  given,  the  student  can  learn  how  to 
take  any  one  of  them  and,  by  mere  inspection  of  it 
as  it  stands,  in  isolation  from  any  context,  point  out 
its  logical  character.  You  are  supposed  to  be  able  to 
say,  by  looking  at  a  list  of  words,  which  of  them  are 
'  general  names,'  *  proper  names,'  '  abstract  names,' 
and  so  on ;  or  by  looking  at  a  list  of  propositions, 
which  of  them  are  {e.g.)  categorical  or  hypothetical. 
You  are  taught,  either  expressly  or  by  implication, 
that  the  logical  character  of  a  word  or  sentence  re- 
mains the  same  throughout  all  changes  of  context ; 
that,  just  as  when  words  are  combined  into  a  sen- 
tence their  outward  form  undergoes  no  change,  so 
with  their  inner  attributes,  or  *  logical  character.' 
Scarcely  a  hint  is  given  that  these  technical  distinc- 
tions are  as  loose  and  shifting  as  those  which  are 
made  in  Grammar  between  {e.g.)  the  substantive,  the 
adjective,  and  the  verb.    As  we  all  know,  words  which 

Keynes  admits  that  **it  is  in  their  character  as  terms  that  names  are  ol 
importance  to  the  logician,  and  it  will  be  found  that  we  cannot  in  general 
fully  determine  the  logical  characteristics  of  a  given  name  without  explicit 
reference  to  its  employment  as  a  term."  At  p.  9  he  finds  that  nanu's  like 
'fW,  Univerae,  and  Sptur  are  '  geiioral '  or  'singular'  according  to  the  uay 
in  which  they  are  used.  At  j).  1*2  he  finds  exactly  the  same  fault  that  wc 
should  find  with  the  distinction  between  'collective*  and  'general'  names, 
pointing  out  that  the  correct  and  really  im|>ortant  logical  antithesis  is  between 
the  collective  and  the  distributive  iise  of  names.  Some  minor  examples  are 
noted  below  at  pp.  254  and  'J6v*<,  and  of  course,  as  we  saw  at  p.  144,  con- 
text must  often  be  considered  in  getting  sentences  into  logical  form.  See 
also  p.  261. 


vn.  IX,  5^  52      KINDS  OF  NAME  OR  TERM 


241 


. 


have  been  sul)stantives  are  frequently  taken  and  used 
as  adjectives  or  verbs,  and  adjectives  or  verbs  are  in 
the  same  w^ay  turned  into  substantives.  Sometimes 
these  changes  are  only  temporary,  and  sound  odd  and 
fantastic ;  but  often  they  remain,  so  that  even  from 
the  grammatical  point  of  view — where  average  edu- 
cated custom  is  the  only  thing  considered— the  same 
word  belongs  to  two  different  classes,  and  we  cannot 
say  which  it  is  when  considered  apart  from  context. 
Such  words  as  conservative  and  liberal  are  familiar 
instances  in  point. 

At  lirst  it  may  seem  strange  that  precisely  the 
same  kind  of  uncertainty  attaches  to  the  much- 
discussed  and  carefully-detined  distinctions  of  Formal 
Logic.  One  is  naturally  inclined  to  expect  a  better 
result  from  all  the  trouble  that  has  been  taken  with 
these  for  so  many  centuries,  and  to  imagine  that  any 
looseness  must  l)e  merely  accidental  and  cannot  spring 
from  the  very  roots  of  the  system.  One  asks  why 
need  the  distinctions  be  so  faulty  ;  why  should  not 
some  simple  mark  or  set  of  marks  be  mentioned  which 
would  serve  to  discriminate  one  kind  of  name  from 
another,  just  as  we  discriminate  kinds  of  material 
ol)jects?  We  can  explain  the  difference  between  a 
horse  and  all  other  existing  animals,  or  between  gold 
and  all  other  known  metals,  in  such  a  way  that  when 
even  a  moderate  amount  of  care  is  taken  we  can  be 
almost  sure  of  applying  these  distinctions  correctly. 
Why  cannot  the  same  be  done  with  the  different 
kinds  of  name  ? 

The  reasons  are  chiefly  two.  In  the  first  place, 
words  are  instruments — instruments  of  assertion — 
and  both  their  logical  and  their  grammatical 
characteristics  depend  upon   the   function  they  per- 

l6 


242 


mE  OF  WORDS  IN  REASONING      i'ARt  hi 


form  in  asserting.     In   the  second  place  custom  in 
the  use  of  words  is  so  ehistic  that  tliere  is  little  or 
nothing  to  prevent  our  using  any  word  indifferently 
for  either  of  two   opposite    logical    or  grammatical 
purposes, — just  as  a  penny  stamp  may  be  used  either 
for  postage  or  for  receipting  a  hill.     There  is  nothing 
to   prevent   our   taking  (<^ 7.)  a  'general'   name   and 
using  it  as  '  proper/  and  vice  versd ;  lor  example  the 
proper  name  Smith  '   and  tlie  verb  to  jerrymander ; 
nothing,  that  is,  except  an  essentially  variable  custom 
with   entirely    undefined   limits  of  authority.      And 
this   fact,  partly  perhaps   l)ccause   it  is  troublesome. 
Formal     liOgic    proposes    and    tries    to    ignore.        It 
follows    the    grammarians'    habit    of    being    content 
to   think   of  the   average   purpose — l.r.    the   average 
context — of  a  given    word,   and   to    class    the   word 
accordingly,  disregarding   the    pMrticnlnr  occasion  of 
its   use,  especially  if  it   happens   to   be   exceptional. 
Formal  Logic  systematically  tries  to  forget  the  fact 
that  it  is  always  particular  o(*casions  that  we  have 
to    do    with    when     any    doubt    as    to    the    logical 
character   of    a    particular    word    has    arisen.       The 
averaore  logical  (diaracter  of  a  word  tells  us  at  most 
what  its  actual  logical  character  jrrohahh/  is, — tells 
us  what  it  looks,  on  its  face,  as  if  it  ought   to   be  ; 
but  when   doubt  has  arisen  we  need  to  go  beyond 
this  first  superficial  answer,  and  to  raise  the  further 
question   whether  it   is  true   of  the  particular  case. 
No  scientific   account  of  the   use  of   words  can   be 
given  until  we  recognise  clearly  that  words  are,  after 
all,  used  on  particular  occasions,  not  on  general  ones  ; 
that,  strictly  speaking,  any  word   may  be   used  for 

'   In  fact,  most  pro|>er  names  are  derived  from  claiss- names  just  iu  the 
way  that  nicknames  are. 


CH.  ix,i<52      KINDS  OF  NAME  OB  TERM  243 

either  of  two  opposite  logical  purposes ;  and  that 
normally  most  words  may  be  so  used  without  even 
committing  any  grammatical  solecism.  Thus  the 
logical  character  of  a  name  is  not  something  fixed 
and  stable,  but  quite  the  reverse.  It  is  function, 
not  structure,  that  determines  logical  character,  and 
the  function  of  words  in  asserting  is  variable.  The 
different  actual  uses  of  names  are  what  Logic  needs 
to  distinguish,  not  difi'erent  sorts  of  name  apart  from 
their  actual  use ;  words  in  their  context,  not  words 
as  Grammar  conceives  them  or  as  they  lie  side  by 
side  in  a  dictionary.  The  latter  distinctions  can 
only  be  of  service  to  Logic  so  far  as  they  help  us  to 
recognise  the  former.  Some  superficial  help  of  this 
kind  they  do  give,  but  it  Ijreaks  doAvn  precisely  in 
those  cases  wdiere  doubt  has  arisen,  those  cases  where 
Logic  begins  to  be  required  to  correct  the  errors  of 
unaided  conmion  sense.  Since  words  are  adaptable 
instruments  of  assertion,  and  are  not  restricted  to 
a  single  function,  we  might  as  w^ell  ask  whether  a 
penny  stamp,  in  the  pocket,  is  a  receipt  stamp  or  a 
postage  stamp,  as  ask  wdiether  a  word,  apart  from 
its  particular  use,  has  this  or  that  logical  character. 

The  technical  distinctions  among  kinds  of  name, 
as  commonly  conceived  in  Logic,  are  loose  in  the 
same  way  as  those  of  Grammar,  and  from  the  same 
causes ;  but  there  the  resemblance  ends.  The  con- 
sequences of  the  defect  are  altogether  different  in 
the  two  cases.  Loose  distinctions  can  do  very  little 
harm  in  Grammar,  since  it  cannot  matter  much 
whether  w^e  class  a  given  word  as  (e.g.)  a  'sub- 
stantive '  or  not ;  nothing  very  important  turns  on 
the  decision.  And  besides.  Grammar  does  not  put 
forward  a  claim  to  do  anything  more  than  strike  an 


i 


m 


244 


USE  OF  WORDS  IN  REASONING      part  hi 


CH.  IX,  §  53      KINDS  OF  NAME  OR  TERM 


245 


average  among  essentially  shifting  and  local  customs. 
Logic,  on  the  other  hand,  cannot  avoid  making  a 
claim  to  go  deeper  than  mere  custom  and  country, 
even  when  it  tries  to  be  as  modest  as  possihie. 
There  is  no  reason  for  its  existence,  as  apart  from 
Grammar  and  common  sense,  if  it  gives  up  all 
attempt  to  make  technical  generalisations  which 
can  he  trusted.  On  their  face  they  are  statements 
about  class  peculiarities.  Such-and-such  a  kind  of 
name,  or  of  proposition,  is  asserted  to  have  this  or 
that  logical  character,  in  contrast  with  other  kinds  ; 
so  that,  given  any  specimen  of  the  class,  you  can 
infer  something  about  its  nature.  For  it  is  only  in 
order  that  we  shall  l)e  able  thus  to  use  the  ireneral- 
isations  that  there  can  be  any  reason  for  makin'*- 
them  ;  and,  as  we  have  seen,  they  could  have  no 
meaning  if  they  were  never  intended  to  be  applied. 
In  ordinary  talk,  and  in  the  freer  kinds  of  writing, 
vagueness  of  statement  matters  little,  because  we  all 
learn  to  make  allowance  for  it ;  indeed  we  should  oet 
nothing  said  or  written  if  we  were  for  ever  perpleximr 
ourselves  with  the  problems  of  strict  definition.  But 
just  where  the  pretence  of  accuracy  begins  this  easy- 
going behaviour  loses  its  justification  ;  and  even  the 
most  elementary  Logic  is  inclined  to  pretend  to  l)e 
accurate.  So  far  as  the  technical  distinctions  of 
Logic  are  rough,  therefore,  the  defect  is  serious.  We 
shall  presently  see  some  of  the  confusion  into  which 
it  inevitably  leads. 

§  53.— Connotation  and  Connotative  Names 

Most  of  the   logical  importance  wliicdi  belongs  to 
the   traditional    distinctions   among   kinds  of  name 


i 


arises  through  their  reference  to  the  distinction 
between  '  connotative '  names  and  others.  For  on 
this  latter  distinction  depends  our  interpretation  of 
the  doctrine  that  all  connotative  names,  and  only 
connotative  names,  are  liable  to  ambiguity.  In 
order  to  interpret  this  with  any  precision  we  have 
to  know  which  names  are  connotative  and  which 
are  not,  and  the  textbooks  accordingly  take  some 
trouble  with  such  questions  as  whether  *  general/ 
*  proper,'  and  *  abstract '  names  are  or  are  not 
connotative.  But  their  trouble  is  largely  wasted. 
Part  of  the  confusion  and  contradiction  shown  in 
the  answers  to  these  questions  is  caused  by  the 
attempt  to  regard  names  in  isolation  from  their 
context,  and  part  by  some  uncertainty  as  to  what  is 
to  be  meant  by  *  connotation.' 

It  is  not  difficult  to  see  that  the  only  sense  in 
which  the  word  '  connotative '  has  any  value  is  when 
it  is  taken  to  mean  simply  descriptive.  According 
to  this  usage — w^hich  w^as  J.  S.  Mill's,^  and  is  now 
generally  adopted  —  a  name  has  connotation  when 
such  name  is  recognised  as  only  conditionally 
applicable  in  concrete  cases ;  that  is  to  say,  as  only 
applicable  to  anything  when  and  while  the  thing  so 
named  is  of  such-and-such  a  nature, — has  such-and- 
such  attributes  or  qualities ;  and  the  connotation  of 
a  name  is  the  complete  list  of  the  attributes  which 
anvthinfj  must  have  in  order  to  deserve  the  name. 

'  No  doubt  Mill  was  not  completely  consistent  in  this  ;  consistency  was 
never  his  strongest  i)oint.  But  the  jmrpose  of  his  distinction  between 
connotative  names  and  others  (as  clearly  shown,  e.g.  in  book  i.  chap.  ii. 
J5  5)  was  to  put  into  two  separate  classes  names  which  do  and  names  which 
do  not  admit  of  definition.  This  fact  has  been  overlooked  by  those  who, 
like  Jevons  {EJrmcntary  L^sftons,  v.)  or  Mr.  Bradley  (Principles  of  Logic, 
book  i.  chaj).  vi.  §  3),  ima^ne  that  by  *  connotation '  must  be  meant 
implication  generally,  and  not  implication  through  the  definition.  See 
also  below,  pp.  247,  248,  257. 


246 


USE  OF  WORDS  IN  REASONING      part  hi 


In  the  most  useless  sense  of  the  term,  the  '  con- 
notation '  of  a  name  is  the  mental  picture,  or  group 
(or  succession)  of  mental  pictures,   that  happens  to 
occur  to  the  mind  of  the  person  hearing  tlie  name, 
or  to  the  person  using  it,  or  to  both  together.       A 
kind  of  excuse  for  supposing  Mill   to   have    meant 
this  may  perhaps  he  found  in  some  of  his  expressions, 
but  the  confusion    seems  to   be  chieHy   due  to   tiie 
fact  that  a  name  which  has  connotation  (in  the  uselul 
sense),  and  vvhicii  therefore,  when  applied  as  a  j)re- 
dicate,    implies    the    attributes    connoted,    does    also 
suggest  corresponding  mental  pictures, — does  '  excite 
ideas,'    as    it    is    sometimes   called.       Such    excuses, 
however,   do   not   amount    to  a  justification.       It   is 
strange  that  any  logician  could   overlook  the   total 
uselessness  of  the  term  'connotation'  when  taken  in 
this  latter  sense,  owing  to  the  fact  that  all  names, 
as  such,  excite  ideas.     There  would  thus  be  nothinfr 
to  contrast  with  connotative  names.      \\\\  should  be 
laboriously    drawing   a    distinction     between     names 
which  perform  their  function  (however  misloadingly), 
and  those  which  are  devoid  of  all  meaning  or  use  ; 
between    names   which   are   really   names  and   those 
which    are    cmly    noises.        In    nonsense  -  books    for 
children   a   few  such    names    occur,    but   as    a   class 
they  cannot  be  said  to  have   importance   for  Logic. 
The  mistakes  against  which  Logic  has  to  help  us  are 
never   caused    by  the   employment  of  words   which 
entirely   fail   to   excite   ideas;    in   the  suggestion  of 
false  ideas,  not  in  the  absence  of  all  suggested  ideas, 
lie  the  real  dangers  of  lano^uacre. 

Confusion  between  these  two  explanations  of  the 
word  'connotative'  produces,  as  such  confusion  must, 
a  crop  of  perplexities  and  contradictions.     Consider, 


cii.  IX,  §  53      KINDS  OF  NAME  OR  TERM 


247 


for  instance,  Jevoiis'  treatment  of  the  question  whether 
proper   names   are  connotative.      He  quotes^   Mill's 
statement  that  they  are  not  so,  and  fails  altogether 
to  see  that  Mill  is  there  merely  defining  the  sense  in 
which  he  is  jxoing  to  use  the  word  connotative,  not 
declaring  an  opinion  on  a  question  of  fact.     Jevons 
speaks  of  Mill's  view  as  ''  probably  erroneous,"  and 
goes  on  to  argue  (as  if  any  one  had  denied  it)  that 
proper   names  have  a  way  of  reminding  us  of  the 
facts  we  happen  to  know  about  their  owners ;    and 
finally  adds,  ''This,  however,  is  quite  an  undecided 
question  ;  and  as  Mr.  i\Iill  is  generally  considered  the 
best  authority  upon  the  subject,  it  may  be  well  for 
the  reader  provisionally  to  accept  his  opinion."    Would 
it  not  be  still  better  for  the  reader  that  he  should  try 
to  understand  Mill's  statement  - — which  is  not  a  state- 
ment of  opinion,  but  a  postulate — rather  than  try  to 
accept,  as  on  Mill's  authority,  a  view  not  held  l)y 
Mill,  and  for  which  the  epithet  "  probably  erroneous  " 
would  be  far  too  lenient?     There  can  be  no  doubt 
that    Mill,   like  every    one    else,   w^ould    never   have 
wished    to   deny    that    proper   names    raise    mental 
pictures.     So  far  as   proper  names    admit  of  being 
clearly  distinguished  from  general  names,^  the  answer 
to  the  (juestion  whether  proper  names  are  connotative 
depends  entirely  on  the  prior  question  whether  we 
prefer  the  useful  or  the  useless  sense  of  the  term. 
If  the  only  connotative  names  are  descriptive  names, 
then  proper  names  (when  used  as  such)  are  not  con- 
notative ;  on  the  other  hand,  if  to  connote  is  to  excite 

1  ElemenOiry  Jjesmns,  v, 

*  See  note,  p.  245  above.  Proi»er  names,  Mill  says,  "are  not  dependent 
on  the  continuance  of  any  attribute  in  the  object,"  and  they  are  therefore 
classed  by  him  as  non-ronnoUtive.  That  is  the  way  he  defines  the  meaning 
and  purpose  of  the  distinction  as  drawn  and  used  by  himself. 

3  The  nature  of  this  distinction  is  discussed  in  next  section. 


248  USE  OF  WORDS  IX  REASONING      i>aiit  hi 

ideas,  then  proper  names,  like  all  others,  are  connota- 
tive,  and  the  whole  value  and  meaning  of  the  dis- 
tinction is  lost. 

Other  writers '  again,  while  intending  to  take  the 
word  *  connotative '  in   the  sense  in  which  ilill  ex- 
pressly claimed  to  use    it,  have    occasionally    failed 
to    distinguish    between    connotation  as   a  group  of 
(jualities  possessed  by  certain  things,   and    connota- 
tion as  a  list  of  conditions  under  which  a  class-name 
is    supposed    to    be    applicable     to    any    particular 
thing, — failed  to  see  that  connotation   (in   the   use- 
ful sense)  is   something  that    belongs   to   the    class- 
name  and  not  to  the  things  named.     Confusion  on 
this  point  often  arises  through  the  fact  that  a  name 
*'  connotes  attributes  "  in  the  thing  named  ;  whence 
it  is  natural  to  think  of  the  attributes  as  ''  forming 
the  connotation  of  the  name."     Such  a  phrase  may  of 
course  be  used  if  we  remember  that  it  is  not,  stric^tly 
speaking,  the  attributes,  but  the  name's  relation  to 
the  attributes,  which  constitutes  the  connotation.     To 
think  of  the  connotation   as   the   list  of  conditions 
under  which  the  name  is  supposed  to  be  applicable 
will  at  any  rate  guard  us  against  wasting  time  over 
certain  confused  ciuestions  which  mav  otherwise  arise 
— for  instance  the  question  whether  *'  the  connotation  " 
means  all  or  only  some  of  the  properties  possessed  in 
common  by  members  of  the  class.     The  extent  of  a 
class  depends  on  the  definition  of  the  class-name,  not 
the  definition  on  the  accepted   extent  of  tlie  class. 
Otherwise  there  could  be  no  rearrangement  of  class- 
names,  no  prol)lems  of  interpretative  definition,  and 
so  the  growth  of  knowledge  would  come  to  an  end. 

»  E.g.  Mr.  E.  C.  Beueckc,  in  Mimf,  vol.  vi.   p.   532.     And  Mill  himself 
was   not  entirely   free  from   the   confusion   liere   noted  :    see,    for  instance 
p.  257  below. 


CH.  IX,  i^  54      KINDS  OF  NAME  OR   TERM 


249 


Perhaps  the  simplest  way  of  avoiding  confusion 
would  be  to  avoid  the  word  '  connotative,'  substituting 
*  descriptive '  for  it.  Instead  of  the  connotation  of  a 
name  we  may  in  the  same  manner  speak  of  its 
fff'fiyiition.  To  define  any  name,  whether  for  general 
purposes  or  with  regard  to  a  particular  assertion,  is 
to  give  its  connotation  ;  that  is  to  say,  to  specify  not 
the  qualities  or  attributes  possessed  by  those  things 
which  happen  to  bear  the  name,  nor  those  which  the 
average  man  may  think  of  when  he  hears  the  name, 
but  those  which  anything  must  possess  in  order  to 
deserve  the  name, — the  list  of  conditions  under  which 
the  class-name  is  applicable  in  concrete  cases. 

§  54. — The  General  Name 

With  the  general  name,  or  class-name,  we  have 
already  made  acquaintance,  and  have  discussed  its 
nature  at  some  length  in  Part  II.  But  the  account 
which  the  textbooks  give  of  it  differs  from  ours  con- 
siderably. In  the  first  place  they  do  not  sufficiently 
ivcognise  the  difference  between  the  two  opposite 
aspects  under  which  the  general  name  may  be  re- 
garded. A  name  may  be  considered  to  get  its  gener- 
ality either  from  the  fact  of  its  naming  a  genus  or 
class ;  or  on  the  other  hand  from  the  diff'erence 
between  its  function  and  that  of  the  proper  name, — 
fnjin  the  descriptive  manner  in  which  it  names  the 
individuals  that  come  under  it,  in  contrast  with  the 
colourless  way  in  which  a  proper  name  (when  actually 
proper  is  used.  The  textbooks,  though  wavering 
somewhat  between  these  two  meanin^js,  incline  rather 
to  the  former  as  giving  the  better  explanation. 
Etymologically,   no   doubt,  it  is   all   that   could  be 


250 


irSE  OF   WORDS  JX  REASOXIXG      part  in 


CH.  IX,  §  54      KINDS  OF  NAME  OR   TERM 


251 


desired,  l>ut  on  other  grounds  its  value  is  more 
doubtful.  What  Loojic  wants  to  know  about  a  given 
name  is  not  whether  it  applies  to  one  thing  or  to 
more  than  one,  but  whether  it  applies  conditionally 
or  unconditionally  to  whatever  it  may  denote, — 
whether  it  has  'connotation'  or  not.  It  is  only 
so  far  as  the  general  name  coincides  with  the  conno- 
tative  name  that  the  distinction  l)etween  jxeneral 
names  and  others  has  logical  importance ;  and  the 
coincidence  is  imperfect,  and  therefore  untrustworthy, 
until  the  assertion  in  which  the  name  occurs  is  also 
taken  into  account.  It  is  merelv  a  loose  ixranimatical 
truth  that  general  names  are  connotativc  ;  any  name, 
general  or  not,  is  connotative  when,  and  only  when, 
it  is  used  either  as  a  predicate  or  as  one  of  the  terms 
of  a  general  assertion,  and  thus  becomes  the  middle 
term  of  a  syllogism.  And  the  effect  of  ignoring  the 
relation  between  the  connotativeness  of  a  name  and 
the  particular  use  to  which  that  name  is  put  in  an 
assertion  is  to  obscure  the  whole  question  as  to  the 
x'vAit  of  demandini;  a  definition.  Formal  Loiiic  thus 
plays  into  the  hands  of  the  quibbler  who  raises  an 
irrelevant  demand  for  a  definition,  as  well  as  of  the 
quibbler  who  seeks  to  evade  the  demand  when  it  is 
relevant. 

And  in  the  next  place  there  is  another  way  in 
which  the  usual  account  is  unsatisfactory.  The 
general  name,  we  are  told,  is  a  name  which  is  *'  capable 
of  being  correctly  athrmed,  in  the  same  sense,  of  each 
of  an  indefinite  number  of  things,  real  or  imaginary." 
Then  either  all  names  are  general  names  or  there  is 
some  class  of  names  that  are  not  capable  of  this 
usage.  Which,  then,  are  these  ?  Obviously  there 
is  a  class — viz.  proper  names — which  are  only  seldom 


applied  in  this  way,  but  still  they  are  perfectly 
capable  of  it,  as  the  substantive  '  boycott '  proves, 
not  to  mention  more  ancient  examples.  And  there  is 
another  class — viz.  singular  names — supposed  to  be 
constituted  by  the  absence  of  this  capability ;  but 
when  we  come  to  inquire  which  they  are  we  find 
they  include  on  the  one  hand  proper  names,  and  on 
the  other  hand  names  which,  though  they  apply  only 
to  a  single  case,  are  nevertheless  descriptive.  Thus 
the  general  name,  when  considered  apart  from  its 
context,  has  no  other  kind  clearly  contrasted  with  it. 
It  is  sometimes  contrasted  with  the  sinG:ular  name 
and  sometimes  with  the  proper  name,  and  only  the 
latter  contrast  has  importance  for  Logic.  There  is, 
for  example,  no  logical  interest  in  the  fact  that  the 
name  '  God '  is  sin<i;ular  to  a  monotheist  and  ireneral 
to  a  polytheist, — no  logical  interest,  that  is,  in  regard 
to  distinctions  among  kinds  of  name,  liowever  useful 
it  may  be  as  a  mere  example  of  a  common  way  in 
which  words  get  different  meanings.'  And  what 
logical  purpose  can  there  be  in  separating,  as  Jevons 
did,^  names  of  substances,  such  as  gold  or  water,  into 
a  class  by  themselves  under  the  title  *  substantial  terms,' 
since  they  are  just  as  descriptive  as  any  general  name 
can  be  ?  Owing  to  this  undecided  way  of  conceiving 
the  kind  contrasted  with  general  names,  the  question 
whether  general  names  as  such  are  connotative  cannot 
l)e  answered  by  Formal  Logic  except  in  a  way  that 
obscures  the  connection  between  connotativeness  and 
the  risk  of  ambiguity.  We  shall  also  see  (§56)  how 
it  confuses  some  of  the  questions  about  the  use  of 
abstract  names. 

*   Keyues'  Formal  Logic,  p.  9. 

2  Not  always,  but  in  the  Principles  of  Science,  vol.  i.  p.  34.     And  Bain 
{Deductive  Logic,  p.  48)  makes  these  into  singular  names. 


252  USE  OF  WORDS  IN  REASONING      partiii 

§  55. — Denotation 

In  our  first  chapter  (p.  42)  it  was  noticed  that  to 
speak  of  *  the  meaning '  of  a  word  -even  wlien  we 
refer  only  to  its  definition  (connotation)  is  at  times 
ambiguous.  A  given  word  may  admit  of  as  many 
different  definitions  as  there  are  different  reasons  wh\ 
we  may  want  the  word  defined  ;  we  may  he  asking 
how  it  is  commonly  used,  or  how  it  ought  to  be 
used ;  and  the  common  usage  of  one  sect  or  locality 
is  not  always  that  of  anotlier,  while  more  than  one 
standard  of  *  correct '  usage  may  easily  be  sugt^ested, 
— grammatical,  technical,  etymological,  as  well  as 
the  meaning  intended  in  some  particular  assertion. 
But  even  when  all  confusion  due  to  this  source  is 
avoided,  the  question  as  to  *  the  meaning'  of  a 
word  is  still  an  ambiguous  question  in  the  case  of 
general  names,  for  both  the  connotation  and  the 
denotation  of  a  general  name  may  with  equal  right 
be  called  its  meaning;  both  its  general  definition 
and  the  list  of  partic^ular  cases  to  which  it  is  applic- 
able or  applied.  In  speaking  of  general  names, 
therefore,  wx  occasionally  need  words  to  mark  the 
two  sorts  of  meaning,  connotative  and  denotative, 
and  the  corresponding  substantives,  connotation  and 
denotation  ;  but  we  do  not  need  the  term  denotation 
for  any  other  purpose.  It  is  quite  unnecessary,  for 
instance,  ever  to  speak  of  the  denotation  of  a  non- 
coimotative  name,— the  word  '  meaning '  is  all  that  is 
needed  there,  since  such  names  have  only  the  one 
kind  of  meaning:. 


CH.  IX,  §  56      KINDS  OF  NAME  OR  TERM 

S  56. — The  Abstract  Name 


253 


The  abstract  name,  as  conceived  by  Formal  Logic, 
is  in  an  even  w^orse  case  than  the  general  name. 
The  perplexity  of  the  textbooks  as  to  whether  ab- 
stract names  are  general  or  singular,  and  whether  they 
are  connotative  or  not,  is  a  standing  reproach  to  the 
present  teaching  system.  And  this  perplexity  is  in 
great  part  due  to  the  habit,  noticed  above  (§  54),  of 
defining  the  general  name  as  a  name  which  applies  to 
members  of  a  germs  or  class — ie.  to  plural  things — 
a  definition  which  tends  to  introduce  confusion  by 
encouraging  us  to  think  of  abstract  names  as  other 
than  general,  and  as  having  either  no  connotation  or 
connotation  in  some  other  sense  than  *  definition.' 

The  technicality  '  abstract  name '  is  borrowed 
ready-made  from  Grammar,  and  is  there  translated 
*  the  name  of  an  attribute,'  as  contrasted  with  the 
name  of  a  thing.  The  distinction  between  attributes 
and  things  is,  however,  much  too  vague  to  bear  any 
pressure.  The  deepest  philosophy  is  unable  to  say 
what  is  a  '  thing '  as  contrasted  with  '  an  attribute  of 
a  thing.'  Certain  names  indeed  there  are  which  are 
perhaps  never  now  regarded  as  other  than  names  of 
attributes,  and  they  may  be  generally  known  (in 
English)  by  being  formed  from  adjectives  by  altering 
the  termination  in  a  few  well-known  ways ;  e.g.  true, 
truth ;  young,  youth  ;  excellent,  excellence ;  hot, 
heat ;  cool,  coolness ;  adverse,  adversity ;  and  so 
on.  Names  of  this  kind  are  what  Grammar  would 
call  abstract,  but  there  is  no  reason  why  Logic 
should  make  a  distinction  betw^een  them  and  the 
adjectives  to  which  they  correspond.  It  follows  from 
what  w^e  saw  in  Part  II.  about  the  nature  of  general 


254  U.'^E  OF  WORDS  IN  REASONING      partiii 

names,  that  all  of  them  suffer  from  ahstractness  {i.e. 
vagueness),  however  concrete  he  the  things  they 
denote.  Indeed,  the  extent  to  whicli  they  suffer 
from  it  is  wholly  independent  of  the  question 
wliether  the  things  denoted  are  concrete  or  not.  If 
an  adjective,  such  as  *  excellent,'  is  indefinite  because 
all  the  things  belonging  to  the  class  must  differ  some- 
what from  each  other,  it  cannot  become  any  more  so 
by  a  mere  change  in  its  termination  or  in  its  gram- 
matical character. 

The  only  escfipe  from  this  confusion  appears  to  be 
to  make  the  distinction  between  abstract  and  concrete 
refer  to  propositions,  not  to  names  without  special 
context.      It   is   interesting  to   notice  how  narrowly 
some  writers  have  missed  seeing  that  it  is  primarily 
a  distinction  among  propositions  {i.e.  among  names 
in   a  context,   or    names  as  used).     Prof.    Bain,   for 
instance,    illustrates    his    remarks    about    '  abstract 
names 'by  means  of  propositi(ms  in  which   abstract 
names  are  used  as  terms,  and  in  one  passage  speaks 
of    these    as    *  abstract    propositions.'^      Even    more 
instructive  is  it  to  find  so  formal  a  logician  as  Dr. 
Keynes-'  approaching  our   view   from  another    side. 
He  sees,  more  clearly  than  Mill  and  Bain,  the  unsatis- 
factoriness  of  the  old  definition    '  ix  concrete  name  is 
the  name  of  a  thing,  while  an   abstract  name   is  the 
name  of  an  attribute  "  ;  he  sees  that  the  distinction 
cannot   be   regarded  as   having    mu<'h    logical    value 
except  where  it  is  made  purely  relative  and  shifting, 
— which  involves  taking  context  into  account.    When 
we   find    this    view    put    forward    in    a    book   which 
attempts  to   "take    no   cognisance"   of   context,    it 
encourages  us  to  hope  that  the  distinction  will  soon 

^  Loffk  {Deduction),  p.  53.  -i  Fixrmal  Lo^c,  pp.  14-16. 


CH.  IX,  §  56      KINDS  OF  NAME  OR  TERM 


255 


t 


come  to  be  widely  recognised  as  applying  (like  that 
])etween  collective  and  general  names,  noticed  above  ^) 
to  names  as  used  in  propositions,  not  to  names  culled 
from  a  dictionary  and  set  by  themselves.  It  is  the 
assertion,  rather  than  the  name, — it  is  only  the  name 
because  used  to  express  the  assertion, — which  properly 
deserves  to  be  called  abstract  or  concrete. 

Our  view  of  the  matter  goes  further  than  this, 
however.  We  shall  have  occtasion  in  the  next  chapter 
to  notice  that  it  is  not  possible  (except  as  a  mere 
guess)  to  look  at  an  isolated  sentence  and  declare 
that  the  assertion  it  makes  is  abstract  (or  *  essential '). 
Whatever  be  the  words  in  which  the  assertion  is 
expressed,  it  is  not  a  purely  akstract  assertion  if  it 
is  intended  to  have  concrete  application,  or  to  face 
the  chance  of  l)einf;  contradicted  in  the  concrete. 
Here  lies  our  difference  from  the  view  taken  by 
i'rof  Bain,  who  appears  to  have  hardly  quite 
broken  with  the  belief  that  the  abstract  name  makes 
the  proposition  abstract,  in  spite  of  his  seeing  that 
abstract  propositions  have  a  concrete  meaning  if  they 
have  any  meaning  at  all. 

When  the  logical  character  of  names  is  made  to 
depend  upon  their  function  in  asserting, — their  actual 
and  not  merely  their  usual  or  average  function — the 
different  sorts  of  name  become  merely  different 
linguistic  devices  of  expression.  We  sometimes 
want,  for  instance,  to  express  a  general  assertion, 
sometimes  to  predicate  about  a  Subject.  And  for 
both  these  purposes  the  class-name  is  a  handy  device. 
But  that  does  not  prevent  our  taking  a  name  which 
is  commonly  used  for  these  purposes  and  using  it 
merely  to  refer  to  S  non-connotatively — which  is  the 

^    l*age  240  note. 


256 


USE  OF  WORDS  IN  REASONING      paiit  hi 


normal  function  of  the  proper  name.  We  do  this,  for 
instance,  whenever  we  use  as  Subject  term  a  nickname 
which  we  think  ill-chosen  ;  and  specially  when  our 
purpose  is  to  say  that  *  A '  is  not  A.  Similarly  tlie 
abstract  name  is  a  linguistic  device,  and  its  purpose 
is  that  of  expressing  concisely  a  general  assertion 
which  would  otherwise  have  a  clumsier  form. 

We  found  a])ove  ^  that  there  are  both  lemtimate 
and  illegitimate  abstract  assertions,  the  former  being 
those  in  which  the  abstract  name  (if  this  verbal  device 
happens  to  be  used  at  all)  is  admitted  to  have  some 
denotation, — to  refer  to  some  concrete  cases, — and  the 
latter  being  those  in  which  an  attempt  is  made  to 
lift  the  assertion  above  all  danger  of  being  disproved 
by  a  contradictory  instance.  To  say  that  an  abstract 
name — e.g.  the  name  *  deceit ' — denotes  an  attribute 
is  merely  a  way  of  evading  the  question  whether  it 
has  denotation  or  not,  in  the  only  sense  in  which 
denotation  is  an  important  thing  to  possess.  A 
better  explanation  would  be  that  an  abstract  name, 
when  used  with  any  meaning  (and  so  with  any  kind 
either  of  denotation  or  connotation)  is  a  general  name 
whose  denotation  and  connotation  are  noticeably 
doubtful ;  its  denotation  being  the  concrete  cases  by 
which  the  truth  of  the  assertion  is  to  be  tested,  and 
its  connotation  being  the  definition  w^iich  covers 
these  concrete  cases. 

Nothing  will  be  gained  by  imagining  that  the 
nature  of  the  abstract  name  is  to  be  easily  under- 
stood, but  at  least  we  may  avoid  in  this  way  getting 
into  a  perfectly  hopeless  tangle.  Such  a  result  is  in- 
evitable if  we  are  content  with  a  grammatical  account 
of  the  kinds  of  name,  and  with  the  doctrine  that  con- 

>   Pages  :J1,  219-221. 


cii.  IX,  .^  5G      KINDS  OF  NAME  OR  TERM 


257 


Crete  names  denote  things  or  concrete  cases,  while 
abstract  names  denote  abstractions  (attributes). 
Grammatically  speaking,  a  general  name  is  a  name 
which  denotes  the  members  of  a  class,  in  opposition 
to  a  singular  name,  which  denotes  an  individual 
thing  or  case.  Now  an  attribute,  considered  as  some- 
thing denoted,  and  therefore  as  some  kind  of  entity,* 
can  hardly  be  identified  with  the  group  of  concrete 
cases  in  which  the  attribute  occurs;  and  since,  in 
order  to  deserve  a  single  name  at  all,  it  must  be  re- 
garded as  the  same  attribute  in  all  these  cases,  we 
should  be  driven  to  call  it  singular.  But  if  the 
abstract  name  is  singular,  what  has  become  of  the 
generality  which  inevitably  belongs  to  any  abstract 
assertion ! 

This,  however,  is  only  one  of  the  contradictions 
into  which  the  grammatical  account  of  the  abstract 
name  is  sure  to  lead  us  if  we  attempt  to  take  it 
strictly.  Suppose  we  try  to  answer  the  question 
whether  *  abstract  names  '  are  connotative.  Since  to 
connote  is  to  connote  attributes,  and  an  abstract 
name  is  said  to  denote  an  attribute,  what,  it  may  be 
asked,  is  there  left  for  an  abstract  name  to  connote  ? 
The  answer  suggested  by  J.  S.  Alill  is  that  as  a  rule 
it  connotes  nothing,  but  that  there  are  *  some  cases ' 
where  an  attribute  mav  be  said  to  have  attributes, 
and  that  the  abstract  name  occasionally  is  in  this  way 
connotative ;  for  example,  the  attribute  slowness  in 
a  horse  may  have  the  attribute  undesir ability. 
But  here  he  evidently  falls  into  the  confusion  noticed 
at  p.  248  above,  departing  from  his  own  account  of 
the  nature  of  connotation.     And  if  this  is  the  only 

*  An  abstract  name  as  the  name  of  '  something '  and  yet  not  the  name  of 
any  '  thing '  forces  us  to  use  the  barbarous  word  '  entity  ' ;  but  that  is  a  small 
matter  compared  to  the  other  difficulties. 

»7 


t 


i 


258 


USE  OF  WORDS  IN  REASONING      part  hi 


way  in  which  an  abstract  name  can  l)e  connotative, 
what  are  we  to  make  of  his  statement  a  little  further 
on/  that  *'  it  is  impossihle  to  imagine  any  proposition 
expressed  in  al)stra(.*t  terms  whi(;h  cannot  be  trans- 
formed into  a  precisely  equivalent  proposition  in  which 
the  terms  are  concrete/'  He  instances  the  translation 
of  '  Thoughtlessness  is  dangerous  '  into  *  Tlioughtless 
actions  are  dangerous.'  If  *  thoughtless  actions  '  is  a 
connotative  name,  and  '  thoughtlessness '  is  its  precise 
equivalent,  there  is  evidently  some  confusion  in  hold- 
ing that  '  thoughtlessness '  is  a  non-connotative  name. 
And  of  (tourse  if  we  are  also  in  doubt  whether  we 
mean  by  a  general  name  the  opposite  of  a  singula)- 
name  or  the  opposite  of  a  proper  name,  and  whether 
we  mean  by  the  *  connotation  '  of  a  word  its  defini- 
tion, or  the  ideas  excited  by  it,  or  all  the  qualities 
possessed  by  members  of  the  class,  we  may  complicate 
the  above  contradictions  still  further.  Until  the 
logical  character  of  names  is  seen  to  depend  on  the 
uses  they  are  put  to  in  this  or  that  assertion,  no 
sense  can  be  made  of  this  elementary  part  of  Logic, 
or  of  any  other  parts  that  depend  upon  it ;  the 
separate  statements  about  the  kinds  of  name  will  not 
fit  together,  and  the  whole  of  our  Logic  will  rest  on  a 
false  foundation. 

»   Vol.  i.  p.  119. 


CHAPTER    X 

KINDS    OF    ASSERTION 

S  57. — *  Logical  Form' 

L\  the  account  that  is  usually  given  of  the  kinds  of 
assertion,  the  excessive  attention  of  Formal  Loo-ic  to 
form  as  a  guide  to  meaning  is  easily  seen.  Here  also 
little  or  no  account  is  taken  of  context,  but  each 
iissertion  is  regarded  as  standing  by  itself,  and  the 
logical  character  of  assertions  is  assumed  to  be  un- 
influenced by  the  purpose  for  which  they  are  used  in 
particular  pieces  of  reasoning ;  a  view  which  is  greatly 
helped  by  the  confusion  between  assertion  and 
sentence.  At  the  same  time  our  natural  tendency  to 
the  latter  confusion  is  also  necessarily  increased  by 
the  systematic*  attempt  to  take  '  propositions '  inde- 
pendently of  their  context ;  for  the  more  we  are  led 
to  look  for  the  logical  character  of  the  proposition 
within  the  limits  of  the  proposition  itself,  the  more 
we  are  restricted  to  the  mere  form  of  the  sentence  as 
decisive. 

It  is  true,  no  doubt,  that  Formal  Logic  would 
never  deny  that  sentences  as  we  meet  with  them  in 
ordinary  conversation  or  in  books  often  need  some 
manipulation  before  we  get  them  into  the  so-called 


260 


USE  OF  WORDS  IN  REASONING      pakt  iii 


CH.  X,  §  57 


KINDS  OF  ASSERTION 


261 


*  logical  form.'  *  But  merely  to  refrain  from  denying 
this  obvious  fact  is  too  negative  a  virtue.  By 
making  light  of  the  real  difficulties  of  translating 
sentences  into  the  required  form,  and  in  other  indirect 
ways  to  be  noticed  presently,  Formal  Logic  greatly 
encouraires  the  view  that  the  lo^jical  character  of 
assertions  depends  on  tlie  form  of  the  sentence  in 
which  they  happen  to  be  expressed. 

In  the  first  place,  in  tlu'  account  that  is  usually 
given  of  predication  the  student  is  not  sufficiently 
warned  of  the  difficulty  of  <leciding  vvliicii  (if  any) 
word  or  words  in  a  ^iven  sentence  is  the  Subject 
term  and  which  the  predicate."  The  fact  is  not 
sufficiently  impressed  upon  him  that  the  order  of 
words  in  a  sentence  is  variable,  and  that  the  same 
meaning  can  usually  be  expressed  in  several  different 
ways.  Of  course  it  is  true  that  (tftcr  a  sentence  has 
been  put  into  logical  form  the  S  and  1*  can  be 
distinguished  by  their  order ;  but  that  is  only  to  say 
that  after  they  have  been  already  distinguished  and 
arranged  in  this  order,  such  is  the  order  in  which  they 
are  arranged.      For  instance    you  put  the  sentence 

*  (Jreat  is  Diana '  into  logical  form  only  after  you 
have  recognised  that  '  great,'  in  spite  of  standing  first, 
is  a  description  given  of  Diana,  not  *  Diana  '  a  descrip- 

'  As  we  noticed  above  (p.  144),  there  is  no  foundation  for  the  claim  that 
any  form  of  sentence  is  more  *  logical  than  others,  except  the  traditional 
custom  of  formal  logicians. 

-  See,  for  example,  Jevons'  Elementary  lASsons^  viii.  There  the  Subject 
is  flatly  ideutitie«l  with  **  the  first  term  of  a  proposition"  and  the  I'redicate  with 
"  the  second  term"  ;  the  proposition  itself  is  identified  with  the  "sentence 
indicative  "  ;  and  scarcely  anything  is  said  about  the  need  of  reducing  to 
logical  form.  In  a  later  passage,  22  i»ages  further  on,  this  subject  is 
treated,  but  only  so  as  to  leave  the  student  under  the  impression  that  with 
a  little  care  any  one  may  analyse  any  sentence  correctly  into  S,  copula,  and 
P  by  mere  inspection  of  its  words.  It  should  be  noted  also  that  some  of  the 
logicians  who  insist  on  quantifying  the  predicate  would  go  so  far  as  to 
express  'Great  is  Diana'  as  'Some  great  is  all  Diana,'  and  to  call  'great' 
the  Subject.      A  reference  is  given  by  Dr.  Keynes  {Forituxl  Logic,  p.  71). 


tion  given  of  '  great. '  And  the  same  holds  good  where 
a  single  word  is  used  to  convey  an  assertion,  or  where 
the  sentence  is  in  any  other  form  than  that  which 
claims  the  name  of  logical.  Such  sentences  can 
always  be  reduced  to  the  required  form,  but  in  order 
to  reduce  them  we  have  first  to  decide — on  some 
other  ground  than  the  order  of  the  words — what  is 
the  Subject  and  what  is  the  Predicate.  And  as  we 
saw  above  (pp.  11  and  144),  even  the  most  formal 
logician  must  occasionally  take  context  into  ac- 
count if  he  is  to  decide  this  with  any  approach  to 
<;orrectness. 

We  noticed  in  §  30  some  cases  where  the  analysis 
into  S  and  P  cannot  be  performed  without  help  from 
the  context.  The  same  difficulty  occurs  also  in 
assertions  which  give  two  names  for  the  same  thinu:, 
— as  '  TuUy  is  Cicero,'  or  *  Hund  is  Dog.'  Although 
the  form  of  such  sentences  is  often  exactly  that  of  *  S 
is  P,'  yet  it  is  highly  doubtful  whether  they  can  be 
intended  as  a  description  of  S ;  on  their  face  they 
mean  either  that  the  two  names  A  and  B  are 
applicable  to  the  same  individual,  or  that  the  two 
words  A  and  B  arc  synonymous  ;  only  the  context, 
and  that  uncertainly,  can  tell  us  which  of  the  terms 
is  intended  as  Subject.  Or  again  there  are  cases 
where  excessive  attention  to  the  form  of  the  sentence 
must  obscure  the  meaning  of  the  assertion.  Take 
such  a  sentence  as  *  Rain  is  likely.'  Presumably, 
•  Rain  '  is  not  the  Subject,  but  is  part  of  the  predi- 
cate, of  the  assertion  which  this  sentence  is  intended 
to  make  ;  almost  its  only  conceivable  intention  is,  not 
to  describe  rain  in  general  as  *  likely '  (or  even  '  likely 
to  come '),  but  to  describe  that  indefinite  Subject  which 
we  sometimes  call  *  It '  (and  by  which  we  here  mean 


li 


262 


U^E  OF  ]VORDt<  IX  REASON IXa      part  hi 


the  weather  in  our  own  nei<^hbourhoo(l)  as  threaten- 


ini^  rain. 


Such  cases,  and  especially  where  no  Subject  term 
is  expressed,  should  be  l)rought  prominently  forward 
instead  of  being  lightly  passed  over.  Besides  their 
value  in  keeping  us  from  confusing  assertion 
with  sentence,  they  may  also  help  us  to  see  an  in- 
sufficiently recognised  fact  about  the  nature  of  any 
predicative  statement, — namely  that  the  predicative 
term  is  the  only  part  of  it  which  can  suffer  from 
ambiguity.  It  does  not  matter  how  vague  our  idea  of 
the  Subject  may  be,  so  long  as  we  know  what  is 
referred  to, — since  the  very  purpose  of  predication  is 
to  add  certain  descriptive  characters  to  something  not 
yet  known  to  possess  them,  and  so  to  remove  some  of 
the  vai^ueness  which  is  assunwd  to  exist.  As  Dr.  Stout 
well  says,^  **  The  subject  is,  so  to  speak,  the  formula- 
tion of  the  question  ;  the  predicate  is  the  answer." 
Thus  all  predication  necessarily  assumes  two  things 
about  the  Subject :  (I)  that  the  audience  already  have 
at  least  some  vaijjue  idea  of  that  which  is  to  be 
described ;  and  (2)  that  they  have  no^  already  so  complete 
an  idea  of  it  as  the  predication  attempts  to  give  them. 
In  every  predication,  the  Subject  is  necessarily  taken 
at  least  as  having  some  known  characters,  and  at  most 
as  being  incompletely  characterised  before  the  predica- 
tion is  made.  A  description  of  something  wholly 
unknown,  and  a  description  of  something  completely 
known,  would  alike  be  meaningless. 

*  Analyticftl  Psifcholooif,  vol.  ii.  p.  214. 


CH.  X,  i^  58 


KINDS  OF  ASSERTION 


263 


?J    58. — Universal,  Singular,  Particular  ; 
Affirmative  and  Negative 

From  the  point  of  view  of  any  Logic  which  is  able 
to  recognise  that  the  same  assertion  may  be  expressed 
in  different  forms  of  sentence,  the  A  E  I  0  distinctions 
are  highly  unsatisfactory.  They  openly  turn  on  the 
form  of  the  sentence,  and  therefore  correspond  only  by 
accident  to  ditferences  of  assertion.  It  should  be  noted, 
however,  that  the  contrast  between  universal  and  par- 
ticular may  have  been,  at  least  partly,  suggested  by  a 
really  important  diflerence, — namely  that  between  a 
generalisation  asserted  and  a  generalisation  denied. 
'  All  S  are  P  '  or  '  No  S  are  P  '  are  forms  often  used  for 
asserting  a  generalisation,  while  '  Some  S  are  not  P  '  or 
'  Some  S  are  P  '  are  corresponding  forms  often  used  for 
denying  a  generalisation.  But  even  when  the  distinc- 
tion is  so  understood  the  names  are  badly  chosen,  since 
the  last  thing  the  *  particular  '  does  is  to  particularise  ; 
the  salient  feature  of  it — i.e.  of  the  answer  *  No  '  to 
the  question  *  Is  it  true  that  all  (or  no)  S  are  P ' — is 
cautious  vagueness.  And  as  for  the  universal,  since 
it  is  made  to  include  indifferently  assertions  about  a 
class  and  assertions  about  a  particular  case  (*  singular' 
propositions),  this  name  helps  to  increase  the  difficulty 
wliich,  as  will  appear  in  §  60,  attaches  to  the  question 
wliether  general  propositions  are  predicative  or  not. 
Moreover,  if  singular  propositions,  affirmed  or  denied, 
are  to  be  classed  along  with  general  propositions 
affirmed,  the  excuse  just  mentioned  for  the  division 
into  universal  and  particular  loses  its  value. 

For  the  contrast  between  affirmative  and  negative 
propositions,  as  the  traditional  Logic  conceives  it,  the 


264  USE  OF  WORDS  IN  REASONING      partiii 

excuses  that  are  made  are  stran«rely  weak  ;  at  least 
any  that  I  have  met  with  are  quite  irrelevant  to  the 
objections  here  brought  against  it.     These  objections 
are    not    against    all    possible    distinctions    between 
affirmative    and    negative    propositions,    but    against 
making    the    distinction    depend    upon    the    copula 
which  happens   to  be  used   in    the  sentence.      Mills 
remarks^  on    this   point,    therefore,    are    beside    the 
issue  ;    no  one  denies  that   there   is  a  diiierence  l)e- 
tween  affirmation  and  denial ;  no  one  has  the  smallest 
desire  to  obliterate  or  obscure  that  distinction,  or  to 
throw  a   shadow   of  doubt    upon    its    reality.      The 
questions    raised    are:    (1)   which    propositions    shall 
be  called   affirmative,  and  which    negative!'   auil   (2) 
what  are  the  respective  advantages  and  disadvantages 
of  putting  the  negation  into  the  predicate  term  instead 
of  into  the  copula  ? 

As  to  the  former  (luestion,  the  choice  lies  between 
making  the  distinction  turn  upon  the  form  of  sentence 
and  making  it  turn  upon  the  meaning  of  the  assertion  ; 
and  we  contend  that  the  latter  course  is  ])referable' 
The  admitted   fact   that   to  every  proposition   there 
corresponds  an  '  obverse '  which  is  equivalent  to  it  in 
meaning,  shows  conclusively  that  the  distinc'tion  as 
drawn  in  the  traditional  Logic  is  not  a  distinction  of 
meaning,  but  of  mere  external  form.     Clearly,  there- 
fore, the  claim  that  there  is  a  useful  distinction  of 
meaning    between    affirmative    and    negative    pro- 
positions—a claim  which  no  one  would  dispute— is 
in   itself  no  argument  in   favour  of  the   traditional 
way  of  drawing  the  distinction.     The  real  interest, 
for   Logic,  centres   in    the   reasons    for  making   the 

l)r'vt^';r^''' •^^^•     '^^'  "^'"^  ^^•*'^^'''   ^  think,  to  the  argument,  of 
/wl/       ^    T^T"^^^*''  ^*^'  '^^^-^^^)  and  ot  Mr.  Carveth   K.ml  (/..„. 
l^eductivc  and  Inductive,  i^  i9).  ^      '    ' 


OH.  x,§58  KINDS  OF  ASSERTION  265 

decision  in  one  way  rather  than  another,  not  in  the 
verbal  forms  which  may  be  used  to  express  it  when 
made  ;  and  the  effect  of  neglecting  or  subordinating 
this  inquiry  is  to  lead  the  student  to  suppose  the 
decision  an  easy  matter,  and  so  to  give  undue  weight 
to  the  grammatical  accidents  of  verbal  expression"^ in 
the  sentence.  Why  should  the  sentence  '  No  men  are 
infallible '  be  called  a  negative  proposition,  when  the 
equivalent  sentence  *  All  men  are  fallible'  is  called 
affirmative  ?  This  is  what  Formal  Logic  is  asked  to 
justify. 

As  to  the  question  whether  the  sentence  denying 
that  S  is  M  should  be  written  '  S  is  not  M,'  or  '  S  is 
not-M/  our  contention  is  that  as  regards  logical  theory 
it  matters  not  how  it  is  written,  so  long  as  we  recog- 
nise that  the  latter  way  of  writing  it  does  not  make 
the  assertion   affirmative.      But  as  regards  the  ex- 
position  of  syllogistic  forms,  there   is   a  reason    for 
preferring   the    negative   predicate   to   the   negative 
copula  ;  it  relieves  the  Syllogism  of  some  of  its  need- 
less complications.     The  admission  that  Celarent  and 
Ferio  are  only  Barbara  and  Darii  in  a  verbal  dis- 
guise does  not  in  the  smallest  degree  interfere  with 
the  admission  that  some  propositions  are  affirmative 
and  others  negative ;  it  merely  reduces  by  half  the 
number  of  separate  syllogistic  forms  which  need  be 
considered.      Thus  we  do  not  dispute  (what   Lotze 
says  ^)  that  every  syllogistic  conclusion  which  could 
be  drawn  from  the  premiss  '  S  is  not-M '  could  also  be 
drawn   from  '  S  is  not  M,'  but  we  merely  recognise 
that  the  converse  equally  holds  true. 

The  chief  reason  why  so  many  writers  cling  to  the 
old  formal  distinction,  which  thus  confuses  the  nega- 

>  r^ik,  §  40. 


n  tl 


It- 


266 


USE  OF  WORDS  IN  REASONING      part  hi 


CM.  X,  {^58 


KINDS  OF  ASSERTION 


267 


tive  sentence  with  the  negative  assertion,  is  suggested 
by  Lewis  Carroll/  and  seems  probable  enough  —  a 
dislike  of  negative  terms.  We  need  not,  indeed, 
call  it  (as  he  does)  either  a  morbid  dread  or  an 
unreasoning  terror,  but  we  may  as  well  admit  that 
the  reasons  against  putting  the  negation  into  the 
predicate,  and  so  being  prepared  to  form  negative 
terms  without  limit,  are  eitlier — as  with  Lotze — due 
to  the  superstition  that  every  predicate  term  must  be 
an  independent  conce/d,  or  else  are  merely  gram- 
matical or  literary  —  such  as  that  the  substantive 
*  unpatriot '  is  not  to  be  found  in  the  dictionary,  or 
has  a  clumsy  appearance,  or  that  tlie  word  '  non- 
conformist '  has  happened  to  acquire  in  coniniun  use  a 
special  restricted  sense.  When  a  speaker  chooses  to 
override  a  local  custom  of  not  usin^j  a  certain  nesative 
term,  or  of  using  it  in  too  narrow  a  sense,  the  negative 
copula  disappears.  And  it  is  of  course  only  distinc- 
tions of  copula  which  give  the  copula  any  claim  to 
attention  ;  when  these  are  removed  the  copula  is,  as 
Mill  very  nearly '  recognised,  a  mere  verbal  sign  that 
a  predication  is  made. 

The  question  how  to  distinguish  between  atiirm- 
ative  and  negative  assertions  (as  contrasted  with 
sentences)  presents  some  difficulty.  All  would  agree 
that  the  abstract  distinction  has  in  view  a  relative 
difference  in  definiteness  of  assertion,  or  risk  taken  by 
the  assertor ;  the  negative  assertion  is  easier,  vaguer, 
and  less  risky,  than  the  corresponding  affirmative  ; 
whatever  other  differences  may  be  included  in  the 
distinction,  that  at  least  is  the  logical  value  of  it, 
the  reason  for  drawing  it  at  all.     But  the  question  is 

*  SyjnMir  Logir,  p.  171. 

*  Expressly,  he  did  recognise  this  (lAMjic,  i.  iv.  §  1),  but  his  criticism  of 
Hobbes,  in  §  2,  seems  scarcely  consistent  with  such  recognition. 


how  to  apply  the  distinction.     Evidently  if  it  is  made 
to  turn   simply  on  whether  the  assertion  gives  the 
answer  yes  or  the  answer  no,  then  every  assertion 
would    be  affirmative  and   negative  at   once.^      For 
every  assertion  answers  *yes'  to  one  of  a  pair  of 
contradictory  questions,  and  *  no  '  to  the  other.     A 
1  setter  way  appears  to  be  to  regard  it  as  a  distinction 
among  kinds  of  question,  rather  than  kinds  of  answer. 
Of  every   pair   of  contradictory  questions   there    is 
usually    one    which,   being   vaguer    than    the   other, 
admits  of  the  answer  '  yes '  on  easier  terms ;  assent 
to  it  may  be  satisfactorily  given  on  a  less  extensive 
review  of  the  facts.     We  can  usually  see,  for  instance, 
that  a  given  rule  admits  of  *  some'  exceptions,  more 
easily  than  we  can  see  the  whole  range  of  exceptions 
which  ought  to  be  recognised.     Or  we  can  usually  see 
that  S  is  not  P  more  easily  than  we  can  see  exactly 
what    kind    of  not-P    it   is.       Such    assertions— for 
(|uestion   and  answer  together  make  an  assertion — 
are  those  which  the  name  '  negative  propositions '  may 
have  always  had  vaguely  in  view,  though,  owing  to 
the  old  confusion  between  sentence  and  assertion,  and 
to  the  consequent  insistence  on   a   negative  copula, 
this  account  of  the  difference  is  far  from  having  been 
always  clearly  accepted. 

There  would  be  some  difficulty,  no  doubt,  in  finding 
suitable  names  by  which  to  distinguish  the  two  kinds 
of  question.  We  can  hardly  call  a  question  either 
affirmative  or  negative,  since  in  a  question  as  such 
there  is  neither  affirmation  nor  negation  involved. 
Nor  would  it  quite  do  to  call  the  one  kind  definite 
and  the  other  vague,  since  (1)  it  is   only  relative 

'  This  is  admitted  even  by  so  formal  a  logician  as  De  Morgan  (Farmal 
Loffic,  i>.  40).  ^      ^ 


268 


Ih^E  OF   WORDS  IX  RKASONING      partiii 


CH.  X,  S  59 


KINDS  OF  ASSERTION 


269 


definiteness  which  is  required,  and  (2)  it  is  only  in 
the  case  of  pairs  of  questions  rehited  in  a  special  way 
that  this  (juality  makes  the  diiierence ;  the  questions 
must  be  ahout  the  same  S,  and  the  .suggested  predi- 
cates must  he  contradictory  terms. 

However,  the  name  matters  little.     The  point  to 
notice    is    that    where  the    opposite    questions    are 
general,  or   refer   to   a   class   by  its  class-name   used 
'  distributively,'  our  distinction   between   affirmative 
and  negative  assertions  corresponds  exactly  to  the  old 
distinction  between   a   universal  and  a  particular  of 
opposite  (quality  (between  A  and  0,  or  between  E  and 
I),  with   the  difference,   however,   that  the  form   of 
sentence  used  does  not  itself  determine  the  meanin<r 
but  is  only  one  indication  of  it  among  others.     There 
are  recognised  ironical  expressions,  for  instance,  where 
the  apparently  vague  word  '  some '  may  make  a  very 
definite    reference,    and    there    are    recognised    over- 
statements  where   the   word   '  all '    is    evidently    not 
intended  to  be  taken  literally. 

When,  on  the  other  hand,  the  opposite  questions  are 
not  general,  but  refer  to  some  particular  case — ejj. 
where  a  proper  name  is  used  for  the  subject,  or  a 
class-name  taken  *  collectively  ' — the  negative  asser- 
tion may  always  be  regarded  as  making  use  of  a 
negative  predicate  term.  This  seems  indeed  to  be 
the  only  excuse  for  drawing  a  distinction  between 
positive  and  negative  terms — a  distinction  which 
Formal  Logic  preserves,  while  admitting  ^  that  from 
its  own  point  of  view  **  it  is  a  matter  of  indifference 
whether  any  given  term  is  materially  positive  or 
negative."  From  the  purely  formal  point  of  view  it 
seems  that  no  better  account  of  the  distinction  can  be 

*  E.g.  Keynes'  Formal  Logic,  p.  52. 


given  than  that  it  turns  on  the  question  whether  the 
name,  taken  apart  from  its  context,  has  a  '  negative 
l)refix,'  in  which  case  words  like  anesthetic,  imme- 
diate, or  non-juror  would  have  to  be  accounted  nega- 
tive, while  pairs  of  terms  like  British  and  Foreign 
would  appear  each  as  positive  as  the  other. 

S  59. —Essential  and  Accidental  Propositions^ 

Tliere  are  signs  that  Formal  Logic  is  becoming 
aware  of  the  unsatisfactory  nature  of  this  distinction. 
Though  Mill  and  Bain— especially  the  latter— seem 
to  have  thought  it  an  easy  matter  to  apply  it  con- 
fidently, more  recent  writers  are  beginning  to 
recognise  that  we  cannot  take  an  isolated  sentence 
and  declare  it  to  be  distinctly  of  the  one  kind  or  the 
other.-  In  the  exercises  arranged  for  l)eginners,  this 
assumption  is  still  commonly  met  with,  but  it  belongs 
to  a  view  of  the  '  essence '  of  things  which  is  steadily 
vanishing  with  the  growth  of  the  modern  conception 
of  classes.  The  question  what  qualities  are  essential 
to  the  class  X  is,  as  we  have  seen,  a  perfectly  open 
question,  except  so  far  as  we  can  agree  to  close  it  for 
the  sake  of  making  a  meaning.  Therefore  we  can 
never  declare,  in  a  downright  or  unconditional 
manner,  that  a  given  statement  about  a  class  X  is 
essential ;  we  can  only  do  so  by  virtue  of  some 
previous  agreement  about  the  essence  of  a  class,  or,  as 

>  The  remarks  here  made  apj.ly  equally  to  the  contrast  between  verbal 
and  real  propositions,  or  analytical  and  syviJietical,  or  explicative  and 
ampliativt.  As  Dr.  Venn  notices,  "these  all  mean  substantially  the  same 
thing,  mdicating  at  most  trifling  differences  in  the  jwint  of  view  from  which 
the  proj)ositions  are  regarded." 

-  Tlie  disability  is,  however,  seldom  if  ever  clearly  traced  to  its  source  in 
the  unstable  character  of  the  '  essence '  of  class-names.  Dr.  Keynes,  for 
instance  (Formal  Logic,  p.  44),  seems  to  regard  it  as  merely  due  to'  the 
limited  scope  of  professedly  formal  Logic. 


i 


^T^R 


!l{< 


M 


270 


USE  OF  WORDS  IN  REASONING      part  iii 


it  is  now  more  usually  called,  its  definition.  Of  course 
there  are  plenty  of  cases  where  this  agreement,  though 
tacit,  may  for  most  purposes  be  taken  for  granted. 
But,  as  we  have  noticed  so  often  already,  Logic  can- 
not be  content  with  loose  talk  ai)out  '  most  purposes,' 
nor  with  doctrines  and  distinctions  which  are  satis- 
factory only  where  there  is  no  dispute.  The  fact 
that  in  all  discussion  we  are  constantly  meeting  the 
doubt  whether  the  question  at  issue  is  a  *  merely 
verbal '  one  or  not,  is  a  measure  of  the  real  difficulty 
which  attaches  to  the  distinction  between  essential 
and  accidental  propositions  when  we  attempt  to  apply 
it.  Just  in  those  cases  where  common  sense  fails  to 
avoid  confusion,  the  traditional  distinction  is  found 
incapable  of  giving  help. 

The  meaninir,  or  idea,  of  the  distinction  is  of 
course  clear  enough  ;  essential  propositions  are  what  we 
have  here  spoken  of  as  *  purely  abstract  statements ' — 
statements  whi(*h  are  ingloriously  safe  from  all 
attack,  and  which  make  no  assertion,  but  at  most  lay 
down  a  postulate  about  the  meaning  of  a  word.  That 
it  would  be  an  excellent  thing  if  we  could  always 
prevent  these  from  being  taken  for  statements  of  fa(it 
is  one  of  the  chief  contentions  of  this  book  ;  l)ut  to 
call  it  an  easy  matter  to  avoid  the  confusion  would 
be  far  more  uncomplimentary  towards  those  who 
habitually  fall  into  it — formal  logicians,  for  instance 
— than  I  think  we  have  any  right  to  be.  In  §  G,  and 
again  in  S  ^0,  we  had  occasion  to  notice  the  part  that 
may  legitimately  be  played  by  abstra(*t  statements 
in  preparing  the  way  for  an  extension  of  knowledge 
— a  circumstance  that  goes  far  to  explain  their  radical 
defect  when  they  are  regarded  not  as  guesses  but  as 
absolute  truths. 


en.  X,  §  59 


KINDS  OF  ASSERTION 


271 


Yet  the  ftict  remains  that  the  traditional  Logic 
enters  into  none  of  these  problems,  and  so  does 
nothing  to  make  the  distinction  less  obscure.  As  we 
saw  in  §  53,  the  remains  of  the  old  conception  of 
classes,  and  the  loose  teaching  about  the  nature  of 
connotation,  are  chiefly  responsible  for  the  perplexities 
with  which  the  textbooks  attempt  to  deal,  on  such 
questions  as  whether  all  the  attributes  possessed  by  a 
class  are  connoted  by  the  class-name,^  or  whether  a 
proposition  like  ''  Homer  wrote  the  Eiad''  is  essential 
or  accidental.  When  the  connotation  of  a  word  is 
seen  to  be  neither  more  nor  less  than  its  definition,  it 
follows  that  all  the  essential  attributes,  and  no  others, 
are  connoted  by  the  class-name.  But  since  there 
may  be  an  inquiry  for  the  particular  definition  as 
well  as  for  the  general  one,  the  accepted  list  of  the 
essential  attributes  of  any  class  is  always  liable  to 
extension  or  contraction.  And  as  to  the  statement 
that  Homer  wrote  the  Iliad,  I  do  not  see  how  the 
question  whether  it  is  essential  or  not  can  arise,  so 
long  as  we  regard  it  as  a  predication  about  an  in- 
dividual named  Homer,  since  the  names  of  individuals 
(when  used  as  Subject)  have  no  connotation  in  the  only 
important  sense  of  that  term,and  therefore  only  o-eneral 
assertions  can  be  essential.  Regarded  as  a  predication 
about  Homer,  it  is  clear  that  i/*we  assume  its  truth 
beforehand  it  does  not  express  a  judgment  at  all,  but 
merely  an  assumption ;  or  if  the  predicate  does 
nothing  to  increase  our  knowledge  of  the  subject,  it  is 
only  a  sham  predication  ;  under  such  an  interpretation, 
and  on  the  further  condition  that  this  'if  holds  true, 
then  of  course  its  defect  is  analogous  to  the  defect  of 

'  The  confusions   involved   in  this  question   are   well  analysed    by   Dr 
Keynes  (Formal  Lo<jlc,  pp.  21-25),  who  himself  keeps  clearly  to  Mill's  sense 
of  the  term. 


If 


w 


hi 


I     I'! 


27*> 


USE  OF  WORDS  IN  REASONING      part  hi 


essential  propositions  at  their  worst.  But  other 
interpretations  are  also  possible  ;  it  may  be  a  predica- 
tion about  *  the  author  of  the  Iliad  J  that  he  is 
*  named  Homer ' ;  or  again,  it  may  be  a  statement 
that  the  name  Homer  denotes  the  author  (or  authors) 
of  the  Riad ;  and  both  these  latter  interpretations 
clearly  allow  the  proposition  to  be  accidental. 

§  60. — Categorical  and  Hypothetical 

Propositions 

When  the  word  *  hypothetical '  is  used  in  its 
widest  sense  ^ — to  include  all  propositions  other  than 
categorical — and  when  cate<]jorical  assertion  is  iden- 
tified  with  predication,  it  follows  that  the  prol)lem 
how  to  distinguish  between  categorical  and  hypotheti- 
cal propositions  is  the  same  as  the  problem  how  to 
define  '  predication ' — a  word  which  we  have  up  to 
this  point  been  content  to  leave  undefined.  As  a  mere 
translation,  *  description  of  a  Subject'  is  sufficient, 
but  the  problem  how  to  mark  off  predication  from  all 
other  kinds  of  assertion,  even  those  most  nearly 
resembling  it,  is  one  of  the  standing  difficulties  of 
modern  Logic,  though  in  the  traditional  system  it 
was  overlooked  or  treated  lightly.  On  the  one  hand 
we  may  be  led  to  admit  that  all  assertions  are 
predicative,  that  assertion,  as  such,  is  categorical ; 
on  the  other  hand,  we  may  see  some  reasons  for  trying 
to  make  a  distinction  between  predicative  and  hypo- 
thetical assertions.  If  we  choose  the  former  alterna- 
tive we  shall  meet  with  assertions  which  are  not 
quite  easily  regarded  as  describing  a  Subject ;  if  we 

*  Dr.  Keynes  gives  a  list  of  some  other  usages  of  the  word,  in  a  note  at 
p.  59  of  his  Formal  Lwjic.  And  in  his  eighth  chapter  he  adopts  a  special 
sense  noticed  below  in  §  63. 


CH.  X,  §  60 


A7.\7>.S'  OF  ASSERTION 


273 


choose  the  latter  we  shall  meet  with  assertions  which 
seem  to  l^elong  to  both  the  opposite  kinds  at  once. 

The  contradictions  shown  in  the  account  the  text- 
books usually  give  of  this  distinction  are  a  further 
instance  of  the  evil  eflects  of  confusing  assertion  with 
sentence  and  of  seeking  for  logical  character  in  the 
mere  form  of  the  words  employed.     The  student  is 
fortunate  if  his  textbook  does  not  lead  him  to  think 
that  a  categorical  assertion  gets  its  categorical  char- 
acter by  l)eing  expressed  in  the  form  '  S  is  P,'  and 
that  the  hypothetical  gets  its  character  by  beginning 
with  the  word  '  if,'  or  some  other  grammatical  device 
for  expressing  a  condition.     The  distinction  is  always 
— tacitly  at  least — conceived  by  formal  logicians  as 
a   distinction    of  form    rather  than   of  meaning   or 
purpose.       Thus  they  talk  of  the   '  reducibility '   of 
hypotheticals  to  categoricals— as  if  an  alteration  of 
form  could  alter  the  nature  of  the  assertion ;  and  they 
talk  of  the  hypothetical  as  being  two  propositions 
joined  together,   thus  assuming  that  it  is  perfectly 
easy  to  distinguish  between  a  simple  assertion  and  a 
compound  or  complex  one.     A  little  reflection  shows 
that  it  is  only  when  assertions  are  identified  with 
sentences  that  the  distinction    l)etween  simple  and 
compound  assertions  can  be  maintained;  that  is  to 
say,    the  distinction    is   merely  grammatical,   of  no 
value  to  Logic  except  so  far  as  we  can  trust  the  half- 
truth  that  the  sentence  and  the  assertion  are  identical. 
How  difficult  it  is  for  Formal  Logic  to  recognise  that 
two    sentences  joined    together   as   antecedent   and 
consequent  clause  can  constitute  a  single  proposition 
niay  be  seen   from  a  definition  of  the  hypothetical 
that  is  still   very  often   given:    *^A  proposition  is 
categorical  if  the  assertion  it  makes  is  absolute  or 

i8 


274 


USE  OF  WORDS  IN  llEASONIXG      part  hi 


downricrht,  as  in  '  All  men  are  mortal '  or  *  Some 
men  are  unwise';  it  is  hypothetical  or  conditional 
if  made  under  a  condition,  as  in  '  Where  ignorance  is 
bliss,  'tis  folly  to  be  wise,'  or  *  If  metals  be  heated 
they  expand."  When  these  hypothetical  are  regarded 
as  single  assertions  we  see  at  once  that  it  is  only  a 
part  of  each  of  them  that  is  made  under  a  condition. 
The  assertions,  each  taken  as  a  whole,  are  as  absolute 
or  downright  as  any  other  assertions  are.  What  is 
true  is  that  the  hypothetical  or  conditional  may 
always  be  divided  into  two  propositions  —  two 
'clauses,'  the  antecedent  and  the  consequent — one  of 
ivhich  is  asserted  wider*  eondition  of  the  other  beiiuj 
trtie;  but  that  is  a  very  ditlerent  matter.  It  can 
hardly  be  seriously  maintained  that  the  hypothetical 
as  a  whole  is  the  same  as  its  own  consetjuent  clause* 
But  even  if  we  do  our  best  to  leave  the  mere  form 
of  the  sentence  out  of  account,  and  endeavour  to 
make  it  a  distinction  of  meaning,  the  conception  of 
propositions  as  self-sufficient  statements,  (juite  in- 
dependent of  their  context — or  as  having  a  meaning 
apart  from  the  function  they  are  used  to  perform  in 
a  piece  of  reasoning — is  fatal  to  clearness.  Admitting, 
as  Formal  Logic  quite  freely  admits,  that  all  assertions 

1  It  is  interesting  to  notice  how  nearly  Mill  escaped  this  confusion.  He 
fell  into  it  where  he  expressly  detined  the  categorical  projjosition,  but  not 
in  explaining  the  nature  of  the  hy}K)thetical.  Half  a  page  before,  and  half 
a  page  after,  he  detined  (i.  iv.  3)  categorical  propositions  as  those  in  which 
**the  assertion"  is  not  dei)endent  on  a  condition  ;  he  admitted  that  in  the 
hypothetical  also  something  is  asserted  unconditionally. 

It  is  quite  safe  to  say,  with  Mr.  Hosanquet  {Loijir,  vol.  i.  94,  95)  that  a 
categorical  asserts  an  aitual  fact  alwolutely,  while  a  hypothetical  asserts  only 
the  consequence  that  follows  on  a  supjiosition.  But  no  such  translation, 
we  must  remember,  tells  us  whether  the  projmsition  '  all  X  are  Y  '  is  in  a 
given  case  a  categorical  or  a  hypothetical.  In  projKjsitions  of  this  type,  as 
Mr.  Bosautpiet  notices,  the  line  of  demarcation  is  at  once  blurred.  Iude(d 
the  value  of  the  distinction  cannot  ]>ossibly  be  undei-stood  unless  the  context 
of  propositions  is  taken  into  account  in  deciding  their  logical  character,  aii<l 
we  give  up  considering  the  mere  form  of  sentence  decisive. 


CH.  X,  §  60 


XlXnS  OF  ASSERTION 


275 


may  be  expressed  in  the  so-called  categorical  form 
*  S  is  P,'  there  are  evidently  distinctions  of  meaning 
among  them  which  it  may  be  important  to  notice, 
and  which  seem  to  suggest  a  purpose  and  value  for 
the  distinction  between  hypothetical  and  categoricals. 
For  instance,  some  are  assertions  of  general  rule, 
while  some  are  assertions  of  particular  fact;  or 
again,  some  imply,  while  others  do  not  imply,  the 
existence  of  S. 

The  difficulty  is  that  if  we  leave  off  making  the 
mere   form   decisive,  and   yet   do   not   make  actual 
function  decisive,  we  are  left  with  nothing  but  average 
function  as  a  guide  in  applying  the  distinction ;  and 
average  function  cannot  l)e  more  than  a  rough  un- 
satisfactory guide.     It  is  true  that  the  majority  of 
assertions  come  before  us  not  as  parts  of  an  expressed 
syllogism,  but  with  an  appearance  of  self-sufficiency, 
and  we  are  left  to  imagine  uses  for  them — to  see 
them  as  potential  major  or  minor  premisses,  ready 
for  use,  and  only  waiting  to  enter  into  combination 
when  the  occasion  offers.      It  is  natural  that  there 
should  be  a  good  deal  of  agreement  as  to  the  special 
use  which  most  befits  a  given  truth  as  it  comes  before 
us,  or  which  is  the  most  pressing  or  obvious  use  to 
make  of  it ;  and  it  is  in  this  way,  no  doubt,  that  we 
draw  convenient  rough  distinctions  like  that  between 
assertions  of  general  rule  and  assertions  of  particular 
fact.     Their  convenience  leads  us  to  forget  their  lack 
of  clearness;   because,   for  instance,  we  can   usually 
recognise  a  statement  of  general  rule  when  we  meet 
with  it,  we  forget  that  every  general  rule  may  also 
be  regarded  as  a  statement  of  particular  fact,  and 
indeed  is  often  used  as  such,  namely  whenever  it  is 
made  into  a  minor  premiss. 


276 


USE  OF  WORDS  IN  EEASONISG      paut  hi 


Again,  the  difference  between  propositions  (in  the 
form  *S  is  P')  which  do,  and  those  which  do  not, 
imply  the  existence  of  S,  is  even  more  perplexing. 
Quite  apart  from  the  extreme  vagueness  of  the  word 
*  existence,'  so  that  existence  of  some  sort  belongs 
inevitably  to  every  nameable  thing  (S),  there  remains 
the  question  how  the  implication  of  existence,  even 
in  a  more  limited  meaning  of  the  word,  is  to  be 
recognised  in  one  proposition  and  yet  not  in  another 
of  the  same  form.  How  are  we  to  distinguish,  for 
instance,  between  the  meaning  '  If  anything  is  S,  it 
is  P '  and  the  meaning  '  There  are  S's,  and  all  of  them 
are  P,'  when  there  is  nothing  in  the  expression  '  All 
S  are  P,'  to  show  which  meaning  is  intended?  In 
predicative  statements,  of  course,  as  opposed  to  hypo- 
thetical ones,  S  is  necessarily  taken  as  having  more 
than  the  vaguest  kind  of  existence,^  but  this  re- 
flection does  not  help  us  until  we  have  got — the 
very  thing  we  are  here  seeking — a  satisfactory  de- 
finition of  the  difference  between  predicative  state- 
ments and  others. 

There  seems  to  be  only  one  way  in  which  these 
ditticulties  are  to  be  conquered,  namely  by  making 
the  distinction  purely  one  of  actual  function,  as 
opposed  alike  to  average  function  and  to  structure 
of  sentence.  It  is  not  until  we  regard  assertions  as 
parts  of  an  argument  that  we  can  properly  under- 
stand their  ditterence  of  logical  character.  We  thus 
identify  hypotheticals  with  major  premisses,  and  cate- 
goricals  with  minor  premisses  and  conclusions,  the 
former  being  (as  we  saw  at  p.  62  and  elsewhere) 
statements  of  general  rule,  and  the  latter  statements 
of  (relatively)  particular  fact.     As  to  the  implication 

1  See  p.  262. 


CH.  X,  §  GO 


KINDS  OF  ASSERTION 


277 


of  existence,  it  is  clear  that  a  major  premiss,  as  such, 
is  a  pure  inferential,  the  only  statement  it  makes 
l>eing  *from  A  follows  C;  to  abstract  a  major 
premiss  from  the  syllogism,  and  to  regard  it  as  a 
proposition  standing  alone,  is  to  abandon  just  that 
assertion  of  the  existence  (or  truth)  of  A  which  it 
is  the  business  of  the  minor  premiss  to  supply.  A 
major  premiss,  or  pure  inferential,  must  be  something 
different  from  the  major  and  minor  premisses  rolled 
together. 

It  should  not  be  forgotten  that  minorless  major 
premisses,  and  majorless  minor  premisses,  have  no 
existence  as  assertions.  Each  by  itself  would  be  a 
sentence  devoid  of  meaning.  Regarded  as  an  asser- 
tion each  exists  only  relatively  to  the  other  ;  each  is 
called  into  existence  for  a  temporary  purpose,  and 
loses  its  logical  character  again  w^hen  put  to  another 
use.  Just  so  it  is  with  inferential  and  predicative 
assertions;  they  are  uses  to  which  any  assertions 
may  be  put ;  they  are  mere  abstractions  from  the 
syllogism.  The  analysis  of  a  conclusion  into  major 
and  minor  premiss  is  not  like  the  analysis  of  a 
physical  compound  into  its  elements,  but  resembles 
rather  the  analysis  of  a  concrete  thing  into  its 
attributes — resembles  it  at  least  in  the  fact  that  the 
parts  thus  distinguished  lack  independent  existence, 
and  in  the  purpose  which  nevertheless  justifies  so 
artificial  an  operation.  When  we  distinguish,  say, 
the  weight  of  a  sovereign  from  its  hardness  and  other 
qualities,  each  of  the  qualities  so  distinguished  may 
serve  as  a  separate  test  by  means  of  which  to  judge 
the  assertion  that  S  is  a  sovereign ;  and  similarly 
when  we  analyse  the  statement  that  S  is  P  into  the 
two  premisses  *  S  is  M '  and  *  i\I  carries  P,'  we  create 


1 


278 


USE  OF  WORDS  IN  REASONING      paut  hi 


two  separate  tests,  the  failure  of  either  of  which 
discovers  a  flaw  in  the  reasoned  judgment.  And 
while  the  question  whether  S  is  M  cannot  be 
discussed  except  on  the  assumption  that  S  exists  (^*.(^ 
is  something  partly  known),  the  statement  that  ^1 
carries  P  involves  the  statement  that  not-P  carries 
not-M — that  if  P  is  non-existent,  M  is  non-existent 
also — when  existence  is  taken  in  any  sense  that 
fjives  a  value  to  the  distinction  between  existent  and 
non-existent.  Only  in  that  vaguest  meaning  in 
which  existence  is  equivalent  to  nameability,  and  in 
which,  therefore,  there  is  no  point  in  claiming  exist- 
ence for  M,  can  a  major  premiss  make  the  claim 
without  stultifying  one  half  of  its  own  meaning. 

The  double  use  or  meaning  of  the  inferential  (in 
its  two  *  contra-positive  *  forms  just  noticed)  is  an 
important  feature  of  it.  A  rule  of  inference  has 
always  a  two-sided  application, — may  act  as  major 
premiss  to  two  different  minor  premisses,  and  so 
guarantee  two  ditferent  conclusions.  It  has  a  choice 
l)etween  two  antecedent  terms,  one  positive  and  the 
other  negative,  and  either  of  them  may  become 
the  middle  term  of  a  syllogism,  while  in  a  predi- 
cative assertion  (as  contrasted  with  a  predicative 
sentence)  it  is  only  the  predicate  which  can  serve  as 
middle  term.  Both  these  truths,  and  especially  the 
latter,  were  much  obscured  by  the  old  rules  of 
conversion,  owing  to  their  pre  -  occupation  with 
sentences.  Sentences  may  often  need  conversion 
before  we  can  see  clearly  how  to  put  them  together 
as  expressing  premisses  in  the  first  figure.  But  with 
assertions  the  case  is  otherwise.  To  predicate  is,  as 
we  have  seen,  to  give  further  information  about  a 
subject  already  partly  known,  and  so  the  predicate 


en.  x,  §61 


KINDS  OF  ASSERTION 


279 


term  is  the  only  assertive  part  of  a  predicative  asser- 
tion. To  find  what  predicative  assertion  is  made  by 
a  given  sentence  is,  therefore,  to  have  already 
performed  upon  such  sentence  all  the  conversion 
(or  other  rearrangement)  for  w^hich  any  use,  in  the 
special  context,  can  be  imagined.  Even  in  the  case 
of  inferentials  it  seems  on  the  whole  better  not  to 
speak  of  their  conversion  (or  contraposition),  though 
their  two-sided  meaning  does  perhaps  give  some 
excuse  for  doing  so.  To  see  a  statement  as  a  premiss 
is  to  have  already  arranged  its  terms  in  the  required 
order ;  so  that,  properly  speaking,  no  premiss  is  ever 
converted. 

§  61. — Modality 

The  inclination  to  confuse  the  consequent  clause  of 
a  hypothetical  with  the  hypothetical  as  a  whole  is 
perhaps  the  chief  relic  of  the  old  distinction  between 
pure  and  '  modal '  propositions  which  modern  Formal 
Logic  has  preserved.  A  considerable  advance  in  the 
recognition  of  the  defects  of  this  distinction  has  been 
made  in  the  last  two  generations,  and  formal  logicians 
of  the  present  day  are  ready  enough  to  leave  out  of 
account  the  old  doctrine  of  modality  as  a  whole.^  If 
you  once  begin  to  count  qualifications  as  modes,  it  is 
extremely  difticult  to  find  any  assertion  that  cannot 
be  regarded  as  a  qualification  of  some  simpler  asser- 
tion which  might  conceivably  have  been  made  in  its 
place.  Any  predication  about  S,  for  example,  might 
be  called  modal  as  compared  with  the  bare  statement 
that  S  *  exists.'  And  even  when  the  conception  of 
modality  is  restricted  to  shades  of  doubt  or  certainty 

*  Dr.  Keynes,  for  instance  (Format/  Lor/ic,  p.  77),  says,  ''The  scholastic 
doctrine  of  modals  may  now  be  regarded  as  obsolete,  and  as  having  only  an 
historical  interest." 


^4 


280 


USE  OF  WORDS  L\  IlKASOXIXG      partiii 


CH.  X,  §61 


KIXDS  OF  ASSERTION 


281 


attached  to  an  assertion,  satisfactory  treatment  of 
them  ))ecomes  quite  unmanageable.^  Moreover  it 
lies  open  to  a  still  more  sweeping  condemnation  ;  for 
it  is  too  evident  that  if  you  identify  *  pure  pro- 
positions' with  assertoric  assertions, — if  you  divide 
assertions  into  assertoric  and  modal  {i.e.  non-asser- 
toric) — you  are  confronted  with  the  question  what 
assertions  are  not  assertoric. 

In  spite  of  the  general  inclination,  however,  on 
the  part  of  our  present  Formal  Logic  to  simplify 
modals  out  of  existence  except  so  far  as  they  can  be 
treated  by  the  Theory  of  Probability,  the  old  concep- 
tion that  modal  assertions  must  be  somehow  contrasted 
with  assertoric  assertions  still  survives  in  connecttion 
with  the  distinction  between  hypotheticals  and 
categoricals,  even  in  subtler  ways  than  the  confusion 
of  a  clause  with  the  whole  assertion.  Remains  of  it 
are  to  be  found,  for  instance,  in  Mr.  \V.  E.  Johnson's 
treatment  of  this  distinction.-  It  is  true  that  he 
avoids  confusing  '  modal '  with  '  non  -  assertoric  ' 
generally,  but  calls  it  "assertoric  on  a  different  plane, 
— concerned  with  the  relation  between  different  sorts 
of  terms."  But  is  this  really  so  ?  Wlien  he  says  that 
the  terms  of  a  modal,  as  contrasted  with  an  assertoric, 

*  As  Dr.  Wim  says  {/Cmpirira/  Lwjir,  p.  241),  "We  have  a  wholo 
cataloi^'iie  of  various  iiualitications :  X  may  Ik?  V  ;  X  is  most  liktly  V  ;  I  do 
not  know  whetlu  r  X  is  Y  or  not ;  and  so  on,  in  cjuite  innnmera»»k'  forms. 
And  the  old  Lope,  reco«,niising  this,  made  a  most  painstaking  hut  supremely 
wearisome  and  ineUettual  attemj.t  to  incori^rate  the  |>rineii.le  underlying 
these  various  forms  into  its  scheme,  in  tlie  doctrine  of  the  so-called  modals. 
.  .  .  Wliat  we  do  now  in  logical  science  is  to  make  a  distinction  between 
those  cases  of  douht  whi.h  admit  of  a  numerical  estimate,  that  is.  those 
which  re.st  u|>on  (piantitative  statistics  ;  and  those  which  are  hoi^dessly 
vague  and  indefinite.  The  latter  we  let  alone.  ...  As  regards  the  former 
our  attitude  is  very  different.  .  .  .  What  we  do  now,  it  need  hardly  be 
said,  is  to  relegate  them  to  the  science  of  Probabilities.  .  .  ."  And  in 
chap.  xii.  of  Dr.  Venn's  Lmjic  of  Chanrc  the  same  view  is  exj.lained  at 
greater  length. 

2  See  J/im/,  1892,  p.  18. 


are  "  the  thinker  and  his  relation  to  some  judgment 
which  is  propounded  to  him,"  we  fail  to  see  in^'what 
respect  his  *  modal '  assertions  differ  from  any  others. 
When  a  judgment  is  made  there  is  always  a  thinker 
involved,  and    a   more  or   less   reasoned   conviction 
on  his  part  that  his  decision  is  justified  on  the  data 
at  present  available.     And  since  the  dogmatic  quality 
of   an    assertion   depends    solely    on    the    assertor's 
attitude  towards  criticism,  there  is  nothing  to  show 
the  amount  of  this  quality  present  in  a  given  case 
until    the   subsequent   criticism    is   incurred.       Mere 
phrases  of  conviction  can  be  no  more  than  rhetorical 
rtourishes,   the  motives  and  meaning   of  which    are 
easily    misunderstood.       To    insist    on    a    difference 
between    *X    is   true'    and   *  any  rational   person   is 
bound  to  assert  that  X  is  true'  is  to  do  the  mere 
form  of  sentence   too   much   honour.       Is   not   Mr. 
Johnson    here    forgetting    a    pithy    and    humorous 
suggestion  of  his  own,'  to  the  effect  that  we  do  not 
increase  the  force  of  an  assertion  by  saying  that  we 
are  quite  certain  that  we  are  quite  certain  that  our 
assertion    is   really   true?      The   claim    to    be   true 
l»elongs,  I  submit,  to  assertions  as  such,  whatever  the 
content  asserted  may  be ;  and  even  if  it  were  possible 
for  any  assertion  to  avoid  making  this  claim,  it  seems 
a  strange  paradox  to  identify  such  a  non-assertoric 
assertion  with  the  '  assertoric  hypothetical'    Besides, 
there    is   no   need   to   drag  in   any   question    about 
modality  for  the  purpose  Mr.  Johnson  has  in  view. 
He    is  distinguishing  forms  of  assertion  solely  with 
regard  to  their  use  in  Symbolic   Logic,  and  he  finds 
that  the  proposition  *If  A,  then  C  adapts  itself  best 

>  See  Mind,  vol.   .xiii.   p.    112.      I  liope  the  literal  inexactness  of  the 
quotation  is  not  here  important. 


i  m  .  n 


I 


^ 


282 


USE  OF  WORDS  IN  liEASOKING      paiit  hi 


CH.  X,  §61 


KIXDS  OF  ASSERTION 


283 


to  the  rest  of  his  system  if  he  takes  it  as  asserting 
merely  a  relation  of  disjunction  between  A  and 
non-C,  and  as  avoiding  *  any  assertion  of  the  direct 
inferential  relation  between  A  and  C.  A  symbolic 
logician  is  perfectly  within  his  rights  in  defining  his 
symbols  as  he  pleases,  and  there  is  no  need  to  cast 
about  for  extraneous  reasons  for  doing  so, — even  if 
the  reasons  themselves  were  good  ones. 

Because  an  assertion  cannot  be  sometimes  true  and 
sometimes  false,  Mr.  Johnson  concludes  {ihiiL  p.  16) 
that  "  the  hypothetical  which  denies  the  conjunction 
of  the  truth  of  the  antecedent  with  the  falsity  of  the 
consequent  is  in  its  turn  denied  by  simply  affirming 
that  conjunction  absolutely."     This  is  no  doubt  true 
of  the  hypothetical  which  restricts  itself  to  so  small 
a  field  of  assertion  ;  a  large  field  of  assertion  is  needed 
to  contradict  it.     But  why  (except  for  the  strictly 
limited  purposes  of  Symbolic  Logic)  is  all   mention 
omitted    of   the    hypothetical    which    has   sufficient 
assertiveness  to   serve  as  a  major  premiss  ?      Tliat 
hypothetical  —  that    interpretation    of  the   sentence 
'  If  A,  then  C ' — instead  of  "  asserting  the  obligation 
to  assert  the  relation  of  disjunction  between  A  and 
non-C"  asserts  a  direct  relation  between  A  and  C 
(or  between  non-C  and  non-A),  namely,  that  'Given 
A's  truth,  C's  truth   follows,'  or  '  Given  C's  falsity, 
A's  falsity  follows.'     The  fact  that  its  contradictory 
asserts  the  possible  instead  of  the  actual  truth  of  a 
certain  conjunctive  is  only  of  interest  to  those  who 
(choose  to  restrict  their  view  to  this  aspect  of  proposi- 
tions,— a  view  in  which  the  function  of  major  premiss 

*  1.0'.  a-s  not  being  eontra<licte<l  by  '  A  may  be  true  without  C  being 
true.'  Mr.  Johnson  seems  to  maintain  that  the  direct  inferential  relation 
between  A  and  C  cannot  be  asserted.  One  naturally  asks,  why  should 
disjunction  be  the  only  relation  i>03sible  ? 


disappears  in  favour  of  other  conceptions  possibly  more 
convenient  for  the  special  purposes  of  Symbolic  Logic. 
There  seems  to  be  a  desire  on  the  part  of  Symbolic 
(and  Formal)  Logic  to  take  the  irreducible  minimum 
of  meaning  as  the  best  interpretation  of  a  sentence. 
And  on  the  assumption  that  context  is  to  be  left  out 
of  account,  there  is,  no  doubt,  much  to  be  said  for 
doing  so.     But  directly  this  assumption  is  given  up 
the  case  is  entirely  altered,  and  we  no  longer  care  to 
put  the  least  possible  meaning  into  a  sentence,  but 
seek  rather  for  the  meaning  actually  intended.     Per- 
haps an  example^   will   help  to   make   this  clearer. 
Take  the  sentence  '  If  A  is  true,  B  is  false.'      We 
cannot   say,    by    mere   inspection   of  this   sentence, 
standing  alone,  whether  the  assertion  intended  by  it 
IS  that  B's  falsity  is  a  legitimate  inference  from  A's 
truth,  or  merely  that  the  double  event  *A  true,  B 
false '  is  non-existent.     But  give  it  a  context  in  the 
shape  of  '  If  A  is  true,  B  is  true  '—that  is  to  say, 
suppose  both  these  propositions  given  true  together — 
then,  since  incompatible  assertions   cannot  be  true 
together,   the  assertions  underlying   these  sentences 
•  annot  be  incompatible ;  we  are  forced,  therefore,  to 
discard  the  former  interpretation  and  to  adopt  the 
hitter.     Now  make  another  supposition,  and  imagine 
that  one  of  the  pair— say  ^f  A  is  true,  B  is  false  '— 
IS  not  given  true  except  upon  some  condition,— e.^. 
'  If  C  is   true.'      Then  our  reason  for  starving  the 
possible  meaning  of  the  sentence  down  to  its  minimum 
is  again  removed,  since,  on  the  hypothesis  that  C  is 
not  true,   the   two    assertions   are   compatible  even 
though  the  direct  inferential  meaning  is  intended. 

•  Some  readers  will  recognise  that  this  example  is  suggested  by  a  logical 
problem  by  Lewis  Carroll  which  appeared  in  Mind,  1S94,  p.  436. 


ii 


:l 


H 


r 


284 


USE  OF  WOIIDS  IX  EEASOXIXa      partiii 


That  this  treatment  of  sentences  as  unstable  in 
meaning  should  be  distasteful  to  the  formal  lofrieiau 
need  cause  us  no  surprise  or  uneasiness.  He  is 
almost  under  compulsion  to  assume  that  the  meaning 
of  a  sentence  is  not  a  matter  for  doubtful  inquiry  at 
all.  In  a  few  particular  cases  he  may  be  driven  to 
admit  the  difficulty,  but  he  nevertheless  clings  to  the 
idea  that  interpretation  is  a  matter  of  certain  simple 
universal  rules.  Such-and-such  a  structure  of  sentence, 
he  conceives,  carries  such-and-such  a  meaning  quite 
apart  from  all  consideration  of  context.  The  restric- 
tion is,  however,  a  purely  voluntary  one,  and  my  con- 
tention is  that,  though  it  may  be  useful  in  Symbolic 
Logic,  it  is  not  to  the  advantage  of  Logic  generally.^ 
We  do  not  best  understand  a  speaker's  meaning  l)y 
insisting  that  he  must  mean  as  little  as  possible.  The 
value  of  any  such  rule  evidently  depends  in  part  upon 
the  question  who  the  speaker  is,  and  what  are  the 
circumstances  in  which,  and  the  purposes  for  which, 
the  speech  is  made. 

To  go  back  to  the  general  distinction  between 
modal  and  assertoric  assertions.  We  hold  that  even 
when  Modality  is  conceived  merelv  as  decree  of 
doubt  or  certainty  entangled  with  the  assertions, 
nothing  can  be  made  of  the  distinction ;  partly 
because  an  assertion  cannot  be  more  than  true,  and 
is  always  problematic  except  so  far  as  its  truth  is 
shown  ;  and  partly  also  because  a  non-assertoric  asser- 
tion (as  distinct  from  a  non-assertoric  sentence)  is  as 
little  conceivable  as  a  round  square.  Something — 
be  it  ever  so  vague — is  asserted  downright,  wherever 
an   assertion   is  made.      It  is  useful,  of  course,  to 

1  So  far  as  Mr.  Johnson  recognises  tliis  (cf.  ibid.  \\  20)  the  objections 
here  raised  attach  merely  to  the  suitability  of  his  system  for  our  purjHJses. 
and  cease  entirely  to  accuse  him  of  error. 


CH.  X,  §  6 1  KIXDS  OF  ASSERTIOX  285 

remember  that  what  looks  like  a  downright  assertion 
may  be  only  a  tentative  expression  of  a  half-formed 
opinion  ;  but  the  use  of  remembering  this  is  merely  to 
guide  us  in  choosing  a  suitable  rhetorical  tone  in 
dealing  with  it  critically.  A  man  whose  assertions 
are  practically  questions  deserves  a  different  kind  of 
treatment  at  the  hands  of  a  critic,  from  one  whose 
chief  anxiety  is  to  beat  down  opposition  or  evade  it. 
Still,  the  distinction  has  nothing  to  do  with  loc^ical 
theory.  If  a  given  '  assertion '  is  not  an  assertion, 
Logic  has  no  concern  with  it  until  it  is  made  so  at 
least  for  the  sake  of  argument. 


\\ 


CH.  XI,  )<  62  KINDS  OF  ARGUMENT 


287 


CIIAI'TER   XI 


kinds  of  argument,  or  rplvsoning 

§  62. — Dkduction  x\ni)  Induction 

In  the  account  tliat  is  given  of  the  nature  of  reason - 
in<x,  excessive  attention  to  form  shows  itself  chietlv 
(as  we  noticed  in  jj  3)  in  the  assumption  that  the 
process  of  reasoning  can  be  separated  from  the 
subject-matter  with  which  the  reasoning  is  concerned  : 
and,  as  a  consequence,  in  the  creation  of  a  body  of 
logical  doctrine  which  practically  leaves  out  of 
account  the  most  important  of  all  sources  of  error  in 
reasoning,  viz.  our  tendency  to  take  *  A '  as  A  too 
hastily,  and  thus  to  reason  deductively  by  means  of 
an  ambiguous  middle  term,  and  to  reach  inductive 
conclusions  from  insufficiently  analysed  facts. 

The  same  assumption  is  largely  responsible  for  the 
distinction  itself  between  Deduction  and  Induction, 
or  at  least  for  the  importance  (other  than  grammatical) 
attributed  to  the  former  branch  of  logical  doctrine. 
Perhaps  the  least  unsatisfactory  account  that  can  be 
given  of  the  distinction  is  that  Deduction  includes 
all  reasoning  in  which  from  given  propositions  you 
draw  a  conclusion  supposed  to  be  contained  in  their 
meaning,  while  Induction  includes  all   reasoning  in 


which  you  reach  a  conclusion  from  observations  of 
fact ;  so  that  the  latter  is  the  interpretation  of  fact, 
while  the  former  is  the  interpretation  of  sentences 
taken  as  true.  Still,  Logic  is  always  concerned  with 
the  detection  oi  faulty  reasoning;  and  since  faulty 
deduction  is  faulty  interpretation  of  sentences  it 
follows  that  any  general  regulative  deductive  prin- 
ciples must  be  of  a  merely  grammatical  nature,  and 
highly  untrustworthy  in  application. 

No  doubt  some  of  the  defects  of  the  distinction 
are  now  w^idely  recognised  even  by  most  of  those 
logicians  who,  for  the  convenience  of  teachers,  separate 
their  books  into  two  portions  called  respectively 
deductive  and  inductive  Logic.  For  instance,  it  is 
pretty  generally  admitted  that  there  is  no  induction 
which  is  quite  independent  of  deductions  from  our 
previous  knowledge,  and  that  the  more  nearly  we 
approach  this  freedom  the  more  nearly  we  get  the 
typical  faulty  induction,— '  empiricar  judgment  on 
too  narrow  a  l)asis  of  fact.  But  the  attempt  to 
preserve  the  distinction  in  spite  of  its  defects  may 
lead  to  much  confusion.  Sometimes,  for  instance,  we 
are  referred  to  the  etymology  of  the  words  deduction 
and  induction,  and  are  told  that  the  former  implies 
an  argument  leading  doivn  from  general  rules  to 
particular  cases,  while  the  latter  implies  an  argument 
leading  on  from  old  know^ledge  to  new.  It  is  true  that 
the  department  called  Deductive  Logic  in  the  textbooks 
is  mainly  devoted  to  the  doctrine  of  the  Syllogism, 
and  to  processes  and  technicalities  subsidiary  to  it ; 
and  that  in  the  typical  syllogism  the  conclusion  is 
narrower  in  range  than  the  major  premiss,  and  there- 
fore in  a  sense  a  step  downward ;  but  on  the  other 
hand  this  same  department  recognises  as  inference 


288 


USE  OF  WOBDS  IX  MEASONIXG      part  hi 


certain    processes   in    which    there   is    no   downward 
movement  of  any  sort,   l)ut  a  mere  recognition  of 
equivalence  of  meaning  under  different  forms  of  sen- 
tence.^    And  as  for  the  arrival  at  new  knowledge,  it 
is  evident  that  induction   has  not  the  monopoly  of 
this,  since  general   rules  are  often  so  loosely  appre- 
hended that  a  deductive  conclusion  from  them  may 
have   all   the  surprise  of  novelty.      Indeed,   formal 
logicians  should  be  the  last  to  forget  this,  since  one 
mistake  that  they  are  habitually  inclined  to   make 
about  the  Syllogism  is  to  exaggerate  the  frequency 
and  importance  of  this  aspect  of  syllogistic  reasoning, 
and  to  suppose  that  the  question  what  conclusion  any 
two  premisses  give  is  generally  so  rich  in  unsuspected 
results  that  it  constitutes  the  chief  syllogistic  prol)lem, 
rather  than  the  (juestion  what  premisses  are  required 
for  guaranteeing  the  truth  of  an   already  proposed 
conclusion..     Probably  this  view  draws  support  from 
the  old    belief  that    Mathematics  is  the  strict   type 
of  reasoning,  instead  of  an  extremely  abstract  and 
artificial   l)rauch  of  it.     Of  course  if  our  facts  were 
certainties  the  case  would  be  different.     The  difficulty 
would  then  be  merely  that  of  remembering  them  and 
putting  them  together  in  large  (juantities,  or  in  com- 
plicated ways.     Since,  however,  the  facts  we  have  to 
deal  with  are  seldom  of  this  convenient  description, 
but  are  themselves  throughout  coloured  with  theory 
— some  of  it  old  and  decayed,  some  of  it  new  and 
untried,  and  all  of  it  open  to  correction — the  restric- 
tion of  Logic  to  the  manipulation  of  complex  symbols 
involves  the  neglect  of  far  more  important  matters. 
The  pressing  practical  need  is  that  of  seeing  that  the 
facts  are  correct ;    it   will  be  time  to  consider  the 

1  Sec  also  §  G4. 


CH.xi,S63  KINDS  OF  ARGUMENT  289 

difficulty  of  massing  undeniable  facts  together  on  a 
large  scale  when  we  have  succeeded  in  getting  the 
undciual.le  facts  to  play  with.     By  far  the  greater 
part  of  our  reasoning,  and  all  of  it  where  the  quality 
of  the  reasoning  is  difficult  to  judge,  is  a  process  in 
which  we  are  constantly  going  back  on  our  '  facts  ' 
forced   to   correct   them    in   details   which   make   L 
ditterence.    In  ordinary  life, and  in  science,  we  normally 
suspect  a  truth  before  we  prove  it ;  our  reasonings 
lag  l)ehind  our  guesses,  and  are  an  attempt  to  review 
the  grounds  of  a  belief  which  has  already  begun  to 
take  si  I  ape. 

Apart  IVom  mathematical  reasonings,  and  from  the 
seldom  occurring  cases  an  instance  of  which  was  quoted 
at  p.  128  n.,  the  only  forward  use  of  the  Syllogism 
IS  where  we  deduce  conclusions  from  a  theory  in  order 
to  compare  them  with  fact ;  indeed,  our  inquiries  into 
the  coui^e  of  Nature  could  not  be  carried  on  without 
a  fre<juent  resort  to  tiiis  process.     But  evidently,  in 
so  far  as  doubt  has  arisen  whether  a  given  conclusion 
IS  reall}-  justified  by  its  premisses,  this  use  of  the 
Syllogism  has  already  ceased  to  be  forward  deductive 
reasoning  and  has  become  reflective.     The  conception, 
tlierefore,  of  syllogistic  reasoning  as  a  movement  of 
thought  from  seen  truth  to  truth  not  yet  seen  applies 
only  to  the  cases  which,  being  comparatively  free  from 
doubt,  are  of  least  importance  to  Logic. 

§  63.— Categorical  and  other  Syllogisms 

From  the  unsatisfactory  formal  distinction  between 
categori(;al  and  other  propositions,  noticed  in  §  60, 
follows  an  equally  unsatisfactory  distinction  between 
categorical  and  other  syllogisms,— those  opposed  to 

'9 


■11 

..  A 


i  i 


290 


USE  OF  WORDS  IN  REASONING      part  hi 


the  categorical  being  either  summed  together  under 
one  name,  such  as  '  hypothetical '  or  *  conditional,'  or 
divided  into  hypothetical,  conditional,  disjunctive,  and 
occasionally  other  kinds.  Both  the  main  division  and 
any  minor  ones  that  may  be  recognised  are  in  Formal 
Logic  made  to  turn  on  the  question  whether  one  or 
more  hypothetical  (or  conditional  or  disjunctive) 
propositions  occur  in  the  premisses.  And  if  what  we 
found  above  be  admitted — that  the  only  hypothetical 
{Le.  non-categorical)  propositions  are  major  premisses, 
and  that  any  proposition,  when  used  as  major  premiss 
and  regarded  in  isolation  from  any  minor,  is  hypo- 
thetical— the  worthlessness  of  these  formal  distinctions 
is  at  once  apparent.  There  is  no  basis  for  them 
either  in  difference  of  chara(-ter  between  different 
syllogistic  arguments  or  in  difference  of  the  meaning 
of  the  rules  for  avoiding  invalid  conclusions. 

To  what  extent  formal  logicians  would  maintain 
that  the  distincttion   between   categorical   and  other 
syllogisms,  or  between  the  various  kinds  of  the  non- 
categorical,  have  importance  for  Logic  and  not  merely 
for  Grammar,  it  is  difticult  to  say  ;  partly  because  it  is 
not  their  habit  to  distinguish  carefully  between  logical 
and  grammatical  doctrines,  and  partly  because  it  is 
so  much  their  habit  to  register  or  preserve  distinctions 
without    raising   the   question    wdiat    use    they    are 
intended  to  serve.     But  we  should  notice  at  any  rate 
that  even  in  Formal  Logic  it  is  recognised  that  some 
syllogisms  may  be  viewed  as  belonging  to  either  of 
the    two    main    kinds    indifferently,    and    that    the 
principles  involved  in  their  recognition  may  easily  be 
extended  to  include  the  other  cases. 

Although  formal  logicians  are  not  entirely  agreed, 
it  seems  safe  to  take  Dr.  Keynes  as  among  the  most 


CH.  XI,  ^  63  KINDS  OF  AUG UMENT  291 

careful  exponents  of  their  view^s.  He  notices  four  kinds 
of  syllogism  opposed  to  the  categorical,  called  respec- 
tively conditional,  hypothetical,  hypotheticO'Categori- 
cal,^  and  disjunctive.  The  first  two  difler  from  the 
third  in  having  no  *  categorical  proposition '  in  them, 
and  difler  from  each  other  according  as  their  three 
propositions  are  '  conditional '  or  *  hypothetical '  in  the 
special  sense  which  (following  Mr.  W.  E.  Johnson)  he 
attaches  to  these  terms,— the  difterence  being  that 
the  antecedent  and  consequent  terms  of  the  '  hypo- 
thetical '  are  propositions,  the  truth  of  C  following 
from  the  truth  of  A,  while  the  terms  of  a  '  conditional ' 
are  predicate  terms  of  the  same  Subject,  so  that  the 
proposition  can  always  be  reduced  to  the  form  *  If  any 
S  is  A,  then  that  S  is  C  Dr.  Keynes  would  apparently 
allow  -  that  the  conditional  syllogism,  and  still  more 
easily  a  syllogism  w4th  only  one  premiss  conditional,^ 
may  be  reduced  to  categorical  form,  or  in  other  words 
ihfl'ers  from  the  categorical  syllogism  only  in  expres- 
sion, not  in  meaning.  He  allows  also  {Formal  Logic, 
p.  302)  that  any  hypothetical  syllogism  may  be 
reduced  to  a  mood  of  the  categorical  syllogism.  There 
remains,  then,  the  'mixed'  syllogism  and  the  dis- 
junctive syllogism.  As  regards  the  distinction  be- 
tween them,  it  seems  to  follow  from  Dr.  Keynes' 
account  {ibid,  ^  141)  of  the  relation  between  the 
*  alternative '    and    the    conditional    or    hypothetical 

'  Formal  Loffic,  p]).  300,  312.  I  will  take  leave  in  this  chapter  to  speak 
of  the  '  hypothetico-categorical '  syllogism  as  the  '  mixed '  sylIo«ism,  for 
brevity.  "^      '^ 

^  That  is  to  say,  lie  allows  {Fontial  I^gic,  p.  217)  that  "there  is  no 
vital  <list motion  "  between  conditional  and  categorical  propositions  ;  and 
(p.  301)  that  distinctions  of  mood  and  figure  may  be  recognised  in  condi- 
tional syllogisms  precisely  as  in  categorical  ones. 

3  Strictly,  this  seems  to  be  a  fifth  kind,  or  rather  to  have  as  much  right 
to  separate  recognition  as  the  other  four  kinds  have.     See  Formal  Louie 
p.  300  note.  ^    ' 


I 


292  USE  OF  WORDS  IN  REASONING      part  in 

proposition  that  liere  also  form  of  expression  alone  is 
concerned;  and  indeed  he  plainly  says  {ibid.  p.  312) 
that  "  the  force  of  an  alternative  as  a  premiss  in  an 
argument  is  equivalent  either  to  that  of  a  conditional 
or  to  that  of  a  hypothetical  proposition."  When  there- 
fore we  look  heyond  merely  grammatical  considera- 
tions, and  ask  what  is  the  value  of  tlie  distinction 
between  categorical  and  other  syllogisms,  we  find  that 
it  is  only  the  mixed  syllogism  which  can  he  supposed 
to  he  importantly  ditierent  from  the  categorical. 

Now  we  must  admit,  of  course,  that  there  is  a 
diflerence  —  which  may  for  some  yjurposes  be  im- 
portant— between  the  assertion  that  if  anything  (S) 
is  M,  it  is  P,  and  the  assertion  that  if  A  is  true,  C  is 
true.  But  the  admission  says  nothing  as  to  whether 
syllogisms  with  the  one  kind  of  major  premiss  are 
importantly  different  from  syllogisms  with  the  other ; 
which  is  the  question  now  before  us.  Dr.  Keynes 
argues  effectively  {ibid.  S  -37)  against  the  view,  held 
by  some  logicians,  that  the  mixed  syllogism  lacks  a 
middle  term  ;  and  finally  remarks  [ibid.  p.  309)  that 
whether  it  can  or  cannot  be  actually  reducted  to  pure 
categorical  form,  it  can  at  least  be  shown  to  be 
analogous  to  the  ordinary  categorical  syllogism.  He 
notices  further  that  the  modus  ponens  and  the  modus 
tollens  are  analogous  to  certain  forms  of  the  categorical 
syllogism,  and  that  fallacies  in  the  mixed  syllogism 
correspond  to  certain  fallacies  in  the  categorical 
syllogism.  But  he  does  not  explain  what  differ- 
ence is  here  taken  to  exist  between  a  (capacity  for 
reduction  to  categorical  form,  and  the  '  analogy '  thus 
recoornised  ;  and  evidently  such  difference  can  depend 
only  on  the  extent  to  which  difference  in  the  mere  form 
of  sentence  is  allowed  to  blind  us  to  identity  of  meaning. 


CH.  XI,  5^6:> 


KINDS  OF  ARGUMENT 


293 


While  we  freely  admit  that  the  distinction 
between  conditionals  and  hypothetical,  as  drawn 
by  Mr.  Johnson  and  Dr.  Keynes,  presumably  has 
importance  for  some  purpose  or  other,  we  must  also 
notice  that  its  defenders  nowhere^  say  quite  clearly 
what  importance  it  is  supposed  to  have  in  producino- 
essentially  different  kinds  of  syllogism.  The  question 
contains  two  separate  inquiries  :  (1)  Is  the  major  pre- 
miss, and  (2)  is  the  minor  premiss  essentially  different 
in  the  two  cases  ?    We  may  take  as  typical  the  forms : — 


( 'oruiifionai  Mixed. 

If  water  is  salt,  it  i.s  X.  If  virtue  is  involuntary,  so  is  vice. 

Sea  wattT  is  salt ;  Virtue  is  involuntary  ; 

.  • .   Sea  vk'ater  is  X.  .  • .   So  is  vice. 

First  as  to  the  major  premiss.  Is  it  denied  that 
both  these  major  premisses,  in  spite  of  their  difference, 
are  '  inforentials,'  and  as  such  perform  exactly  the 
same  function  in  the  respective  arguments'^  The 
fact,  noted  by  Dr.  Keynes  {ibid.  p.  220),  that  we 
may  have  sentences  in  hypothetical  form  which 
have  no  inferential  meaning,  is  not  relevant  unless 
form  instead  of  function  be  taken  as  decisive.  The 
question  remains,  how^  can  any  proposition  serve  as 
major  premiss  unless  it  contains  the  positive  assertion 
that  A  carries  C.  Of  course,  as  we  noticed  just  now 
in  §  61,  a  symbolic  logic  may  be  invented  which,  for 
some  purpose  of  its  own,  limits  the  meaning  of  the 
statement  that  from  the  proposition  A  the  proposition 
C  follows,  so  as  to  exclude  the  inferential  meaniuGf 

*  The  mere  fact,  noted  by  Dr.  Keynes  {ibid.  p.  301)  that  the  translation 
of  the  mixed  syllogism  into  pure  categorical  form  is  more  difiicult  than 
where  the  major  [iremiss  is  a  *  conditional '  cannot  be  relevant  unless  no 
translations  except  oasy  ones  are  to  be  allowed, — a  rule  which  Formal 
Lf)gic  no  doubt  tends  to  act  U})on,  but  which  it  can  scarcely  uphold,  or  even 
interpret  satisfactorily. 


294 


USE  OF  WORDS  IN  REASONING      taut  hi 


CH.  XI,  §  63 


KINDS  OF  ARGUMENT 


295 


altogether.^  But  Mr.  Johnson,  in  the  passage  referred 
to  above,  is  talking  of  '  propositional  synthesis,*  where 
the  problem  is  to  put  together  any  two  or  more 
propositions  and  to  read  their  combined  meaning ; 
and  evidently  two  propositions  may  have  a  combined 
meaning  even  when  they  do  not  state  the  relation 
of  a  particular  case  to  a  general  rule,  and  where 
accordingly  there  is  no  major  premiss  involved  in 
the  process  at  all.  If  I  add  the  statement  '  The 
conjunction  of  A  true  with  C  false  is  false'  to  the 
statement  'The  conjunction  of  A  true  with  C  true 
is  false,'  they  together  involve  the  statement  that  A 
is  false,  but  the  process  has  nothing  in  common  with 
Syllogism,  either  as  here  understood  or  as  it  is  under- 
stood in  Formal  Logic  generally, — nothing,  that  is, 
except  the  fact  of  containing  three  propositions;,  one 
of  which  is  derivable  from  the  other  two.  Uur 
contention  is,  not  that  every  process  of  propositional 
synthesis  requires  an  inferential  major  premiss,  but 
that  such  is  required  for  every  combination  that 
comes  under  the  dictum  de  omni  et  nullo  in  its 
widest  interpretation ;  and  that  it  is  required  equally 
whether  the  premisses  happen  to  be  expressed  in 
(categorical  form  or  not.  For  instance,  with  the 
minor  premiss  '  virtue  is  involuntary '  you  cannot 
get  the  conclusion  *  vice  is  involuntary '  unless  your 
major  premiss  does  something  more  than  merely 
deny  the  truth  of  the  conjunction  *  A  non-C ' ;  such 
denial  cannot  operate  to  connect  the  minor  premiss 
with  the  conclusion  unless  we  proceed  beyond  it  to 
the  positive  assertion  that  from  the  truth  of  A  the 
truth  of  C  is  inferrible. 

1  This,  a.«  we  saw  above,  is  what  Mr.  Johnson  appears  to  intend  when 
he  pioi)08es  to  take  it  as  simply  aasertinj,'  the  falsity  of  a  certain  conjunction, 
— the  conjunction  of  A  true  with  C  false. 


It  is  therefore  in  the  minor  premiss,  if  anywhere, 
that  we  must  look  for  possible  reasons  for  the  dis- 
tinction between  the  two  kinds  of  syllogism.  No 
doubt  there  is  a  ditierence  between  the  assertion  '  S 
is  M '  and  the  assertion  '  A  is  true ' ;  ^  but  we  are 
seeking  for  important  difference,  not  merely  for 
difference  at  large.  In  what  important  respect  do 
the  two  kinds  of  minor  premiss  differ?  If  one  of 
them  is  a  predication  and  the  other  not,  the  difference 
would,  I  admit,  be  important ;  but  is  this  the  case  ? 

The  answer  is  implied  in  our  remarks  about  pre- 
dication in  SS  30  and  57.  If  there  is  no  need  that 
the  sentence  expressing  a  predication  should  contain 
any  definite  Subject  Term,  then  *A  is  true'  may 
very  well  be  the  predicate,  and  the  Subject  remain 
unexpressed,— just  as  in  the  statement  '  Fire  ! '  And 
if  it  is  taken  to  be  the  predicate,  then  the  'mixed' 
syllogism  is  seen  at  once  to  be  a  mere  accidental 
variety  of  the  typical  form  Barbara.  The  question 
what  is  the  best  expression  that  can  be  found  for 
the  unexpressed  S  is  never  of  much  importance,  since 
in  predication  as  such  [i.e.  as  opposed  to  a  statement 
about  '  All  S '  when  used  as  major  premiss)  the 
definition  of  S  is,  as  we  saw  at  pj).  262  and  276, 
irrelevant.  The  predicate  term  is  the  only  interest- 
ing part,  just  as  it  is  the  only  dangerous  part,  of 
any  predication, — of  any  statement  which  is  not  an 
inferential  in  disguise.  Some  writers^  have  suorcrested 
that  where  all  attempts  to  specify  the  Subject  fail, 
we  may  be  content  to  make  '  Reality '  into  one,  and 
to  say  'Reality  is  such  that  A  is  true.'  Another 
suggestion  of  the  same  kind  is  referred  to  by  Dr. 

'   Except  where  the  proposition  '  A  '  says  '  S  is  M.'     See  p.  281. 
2  E.g.  Mr.  Bosanquet,  Ijogic,  vol.  i.  p.  78. 


ii 
H 


(I 


296 


USE  OF  WORDS  IN  REASONING      paktiii 


Keynes,'  where  the  minor  premiss  is  expressed,  *  The 
actual  case  is  the  case  of  A  beintij  true.'     Dr.  Kevnes 

CI?  ^ 

adds  that  this  is  not  really  satisfactory,  hut  he  does 
not  tell  us  why.  Of  course  no  such  phrases  can 
pretend  to  be  the  only  possible  expressions  for  so 
vague  a  Subject  ;  nor  again  can  it  be  claimed  that 
these  circuitous  ways  of  saying  'A"  have  bterary 
excellence  of  any  kind.  But  the  same  Hterary  defect 
attaches  to  many  other  translations  into  logical  form, 
even  when  Formal  Logic  considers  them  satisfactory. 
No  such  translations  need  claim  anything  more  than 
an  explanatory  value,  such  as  J)r.  Keynes  himself 
seems  to  allow  to  the  second  of  the  two  just  (pioted, 
when  he  says  "  it  is  worth  giving  in  order  to  bring 
out  the  analogy  between  the  above  example  of  th(» 
modus  ponens  and  the  (categorical  syllogism  in 
Barhara.  The  only  reason  for  here  referrin<r  to 
these  uncouth  forms  was  to  answer  the  question 
whether  this  analogy  exists. 

It  may  still  be  asked  whether,  even  admitting' 
that  there  is  no  difference  of  essential  charact(T 
between  the  framework  of  categorical  syllogisms 
and  that  of  any  others,  the  difference  in  the  rules 
for  avoiding  invalid  conclusions  does  not  perhaps 
amount  to  a  reason  for  preserving  the  distinction. 
They  are  difierent  sets  of  rules,  certainly,  and  those 
which  are  used  for  the  categorical  syllogism  are 
much  more  complicated  than  the  others.  But  there 
is  no  special  virtue  in  complicated  rules  where 
simpler  ones  are  equally  effective,  and  it  is  demon- 
strable that  the  two  rules  of  the  '  mixed '  syllogism 
may  be  reduced  to  a  single  one,  and  that  that  one 
is  sufficient  for  guarding  against  every  invalid  cate- 

'  Formal  Logic,  p.  304. 


CH.  XI,  i^  63  KINDS  OF  ARGUMENT 


297 


gorical  mood.     This  single  rule  is  that  no  apparent 
syllogism  is  valid  unless  there  is  complete  connection 
between  S  and  P  through  M.     Thus  with  the  major 
premiss  *  X  carries  Y  '  (or  *  non-Y  carries  non-X  '),  any 
minor  premiss  which  predicates  either  non-X  or  Y 
fails  to  establish  connection— fails  equally,  and  for 
the  same  reason.     Our  calling  the  fallacy  'affirma- 
tion of  the  consequent,'  or  on  the  other  hand  '  denial 
of  the  antecedent,'  depends  upon  the  meie  accident 
which   of  the   two   equivalent  forms  of  sentence  is 
used  for  the  major  premiss. 

In  applying  this  rule  to  the  categorical  syllogism, 
we  must  remember  that  we  are  only  inquiring  whether 
its  eft'ect  is  the  same  in  guarding  against  invalidity, 
not   whether   it  can   be   directly  and  easily  used  in 
connection  with  the  rest  of  the  complicated  machinery 
of  that  system  as  handed  down.     We  are  therefore 
free    to    adopt    the    interesting  simplification  of  the 
rules  which   has  been    worked  out   by   De  Morgan, 
Keynes,    and    Johnson,    the    results    of    which    are 
summed    up   by   Dr.    Keynes  in  §    152   of  Formal 
TjO(ju\       We  there  find  the  rules  reduced    to   two: 
(a)    M    must    be   distributed,    and    (y9)   to   prove   a 
negative    ('onclusion   one  of   the  premisses  must  be 
negative.       And   he  has  also  shown   that  the  onlv 
mood  rejected  by  (;8),  and  not  also   rejected  directly 
or  indirectly  by  (a),  is  AAO  in  Fig.  4. 

Now  in  the  first  place  as  regards  undistributed 
middle.  It  is  plain  that  the  essence  of  this  defect 
is  the  lack  of  complete  connection  through  M.  When 
reduced  to  Fig.  I,  syllogisms  with  undistributed 
middle  have  their  major  premiss  either  '  particular,' 
or  else  with  non-M  for  antecedent,  while  M  is  the 
predicate   of  the   minor.       But   the    major    premiss 


I 

I'" 


298 


USE  OF  WORDS  IN  REASONING      part  hi 


'  Some  M  are  P '  can  only  become  a  statement  of 
general  rule  if  the  '  some '  are  specified  as  a  class — 
say  XM ;  and  then  M  as  predicate  in  the  minor 
premiss  is  too  vague  to  establish  the  required 
connection,  since  any  S  would  be  correctly  called 
M,  even  if  the  fuller  description  *  xM '  were  also 
correct.  Virtually,  therefore,  in  these  cases  M  is 
not  shown  to  be  the  same  in  both  premisses,  and  so 
the  connection  is  not  established.  And  a  virtual 
identification,  as  opposed  to  a  merely  formal  one,  is 
what  we  were  trying  to  find. 

In  the  second  place,  let  us  look  at  the  recalcitrant 
mood  AAO  in  Fig.  4,  the  one  exception  among  the 
232  invalid  moods  which  are  theoretically  possible. 
If  we  leave  its  conclusion  as  it  stands  (in  order  to 
keep  its  S  the  same  as  that  of  the  minor  premiss), 
there  is  only  one  way  of  reducing  the  premisses  to 
Fig.  1,  namely,  by  converting  both  of  them  ;  the 
minor  premiss  must  be  converted  per  accidens,  but  the 
major  premiss  may  be  converted  either  per  aecidens 
(in  which  case  we  get  an  undistributed  middle) 
or  by  ('ontraposition,  in  which  case  we  get  an  even 
more  evident  l>reach  of  our  rule  against  disconnection 
through  M.  So  translated,  its  minor  premiss  pre- 
dicates M  of  '  some  S,'  while  its  major  premiss  tells 
us  only  that  iion-M  carries  non-P. 

It  seems  stran^re  that  AAO  in  ¥icr,  4  should  be 
the  sole  exception  to  the  rule  that  undistributed 
middle  includes  all  syllogistic  fallacy,  but  Dr.  Keynes 
is  probably  right  in  saying  that  from  the  strictly 
limited  point  of  view  of  Formal  Logic  this  mood 
cannot  be  shown  as  necessarily  involvins^  (even 
indirectly)  a  breach  of  the  rule.  It  remains  true, 
however,  that  our  explanation  in   chap.  i.    (p.    15), 


cu.  XI,  §  63 


KINDS  OF  ARGUMENT 


299 


accounting  for  the  plausibility  of  a  conclusion  drawn 
through  an   undistributed  middle,  will  also  account 
for  the   plausibility  of  any   invalid  mood,  since  the 
question  there  raised  was   quite  independent  of  the 
formal  logician's  question  whether  the  traditional  six 
rules  can   be   reduced  to  one,   or   whether  all  con- 
ceivable   invalid   forms   can   be  accused    of  a  single 
defect.     Evidently  a  large  number  of  the  232  invalid 
forms  can  in  no  way  be  considered  likely  to  occur. 
AAE,    for    example,    in    any   figure,    could    hardly 
deceive   even   the  least  initiated  reasoner ;  nor  any 
E  conclusion  with  two  affirmative  premisses,  nor  any 
universal  conclusion  with  two  particular  premisses.^ 
Indeed,   if  we  think  of  the  way  in  which  the  long 
list  of  invalid  forms  is  arrived  at,  we  see  at    once 
that  there  can  be   no  reason  to  expect  plausibility, 
or  therefore  to  inquire  after  its  causes,  in  all  of  them. 
Ilieir  recognition  as  possible  has  nothing  to  do  with 
an  opinion  as  to  their  likelihood  ;  the  256  moods  out 
of  which  they  are  the  discarded  majority  are  mere 
combinations  of  the  four  letters  AEIO  in  groups  of 
three,  so  as  to  make  64  possible  variations  of  order, 
which  are  then  expressed  in  the  four  different  figures, 
and  so  multiplied  again   by  four.     The  meaning  of 
the  propositions  has  nothing  to  do  with  the  arrange- 
ment;  as  far  as  that  goes  the  letters  AEIO  might 
just  as  well  be  drawn  from  a  bag.     Hence  it  would 

^  We  cannot,  however,  make  any  satisfactx)ry  list  of  the  invalid  moods 
which  are  i)lausible— since  this  quality  varios  both  with  the  subject-matter 
and  with  the  person  concerned.  Thus,  even  apart  from  subject-matter, 
one  who  would  judge  a  syllogism  more  by  its  sound  than  its  sense  might 
accept  (in  Fig.  1)  EEE,  III,  or  000,  while  others  who  think  at  all  of  the 
meaning  would  be  proportionately  less  inclined  to  accept  them.  Others  again 
might  be  half  tempted  by  the  sound  of  a  mood  like  EEE  or  lAA  (Fig.  1), 
but  might  yet  just  reject  them,  and  compromise  on  EEO  or  lAI  as  safer! 
And  some  beginners,  I  almost  suspect,  when  sufficiently  driven  to  distrac- 
tion, will  choose  a  conclusion  for  a  pair  of  premisses  on  the  principle  that  it 
IS  probably  correct  iu  Logic  because  it  is  evidently  absurd  in  common  sense. 


300 


mK  OF  JFOJiDS  IK  JIEASOXING      part  hi 


be   a    miracle   if  all   of  them   (!Ould   he   reirarJed   as 
pieces  of  actual  reasoning. 

But  at  the  point  where  ^uessinjr  or  ballotin<' 
ceases,  and  thought  comes  in,  the  need  arises  for 
some  vera  causa  as  a  misleading  influence.  And 
since  in  a  valid  syllogism  the  conclusion  is  contained 
in  the  meaning  of  the  premisses,  the  only  rational 
explanation  of  an  invalid  syllogism  seems  to  he 
that  premisses  which  do  not  contain  the  conclusion 
are  imagined  to  do  so  l>y  misinterpretation.  After 
senten(-es  have  been  put  into  'logical  form,'  the 
subtlest  and  most  effective  of  all  sucii  misinterpre- 
tations are  some  of  those  due  to  ambiguous  middle 
(one  form  of  whi(th  is  undistributed  middle),  but 
next  in  importance  to  them  come  the  various  modes 
of  faulty  transhition  of  sentences,  among  which 
these  five  seem  to  be  the  chief  ones :  simple  con- 
version of  A  ;  or  again  of  0  ;  the  supposition  that 
*  some '  means  '  some  only  '  :  or  again  that  '  No  X 
are  Y '  implies  '  All  not-X  are  Y  '  ;  or  again  that  '  All 
X  are  Y '  implies  that  Y  extends  beyond  X,  and 
that  therefore  some  Y  are  not-X.  This  last  is 
perhaps  the  likeliest  explanation  of  AAO  in  Fig.  4. 
A  glance  at  Euler's  diagrams  for  this  mood  will 
show  that  its  defect  as  a  piece  of  reasoning  consists 
merely  in  overlooking  the  bare  possibility  that  8, 
M,  and  P  are  coextensive.  One  at  least  of  its  pre- 
misses is  held  to  include  a  converse  0  proposition,  and 
thus  the  mood  is  mistakenly  brought  under  Baroko 
or  Bokardo.  A  rather  less  simple  but  equally 
possible  explanation  is  that  the  minor  premiss  is 
converted  jx^r  accidens,  and  then  the  *  some  '  inter- 
preted as  *some  only '—which  would  involve  'Some 
S  are  not-lM,'  and  so  create  Baroko  fictitiously. 


c-ii.  XI.  S  64  KJXDS  OF  ARGUMENT  30 1 


8  04.  -Mewate  axd  Immeuiaie  Infehknce 

Another  most  uusatisfactoiy  distinction,  due  to 
excessive  attention  to  external  form,  is  that  between 
nie<iiatu  and  mimediate  inference.     Unless  it  is  left 
purely  abstract,  and  not  applied   to  actual  pieces  of 
judgment,  it  depends  on  the  false  assumption    uni- 
vensally  made  in  Formal  Logic,  that  there  can  'be  no 
dirticulty  in  saying  what  is  a  '  single  proposition,'  as 
contrasted  with  '  two  or  more  propositions '  • '  and  it 
necessarily  leads  Formal  Logic  either  to  decline  certain 
mquiries  int.,  the  nature  of  inference,  or  at  least  to 
enter  into  them  in  a  half-hearted  manner.     The  chief 
of  these  in.iuiries  are  ( I )  as  to  the  diflerence  between 
inference  an<l  mere  interpretation  of  sentences,  and  (2) 
as  to  whether  inference  without  mediation  ever  occurs 
In   regard  to  the  former  of  these  questions    the 
piacuce  of  Formal  Logic  seems  to  be,  while  generally 
a.ssumin,u  that  the  sentence  is  the  same  as  the  assertion 
to  be  shy  of  pushing  the  consequences  of  this  assump- 
tion quite  to  their  extreme  ;  and  hence,  while  generally 
assuming  that  translation  from  one  form  of  sentence 
to  another  is  inference  from  one  assertion  to  another 
nevertheless  to  hesitate  about  allowing  this  in  every 
conceivable  case-though  the  exceptions  are  nowhere 
(tiearly  stated.      For  instance,  many  formal  logicians 
would  decline  to  allow  that  the  change  from  '  If  metals 
are  heated,  they  expand  '  to  •  Heated  metals  expand '  is 
an  inference,  and  yet  all  of  them  would  say  unhesitat- 
ingly that  there  is  an  inference  when  you  take  the 
sentence  '  No  black    things  are  white,'    and  turn  it 
round  so  that  it  reads  '  No  white  things  are  black.' 

*  Cp.  pp.  117,  143,  273. 


f:^ 


302  USE  OF  WORDS  IN  REASONING      part  iii 

Similarly,  if  you  take  the  sentence  Mames  is  not 
sober,'  and  by  means  of  a  hyphen  alter  it  into  '  James 
is  not-sober,'  there  again  you  have  got  *  another 
proposition.'  And  apparently  some  formal  logicians 
(see  above,  pp.  281,  295)  hold  that  'S  is  ?'  is  a 
different  proposition  from  *  It  is  true  that  S  is  V  ; 
but  whether  they  would  speak  of  inference  from  one 
of  these  to  the  other  is  a  t[uestion  which  1  do  not 
remember  to  have  seen  answered. 

Of  course  the  chief  explanation  of  this  apparently 
arbitrary  distinction  is  that  the  first  and  the  last  of 
the  above-quoted  transformations  are  not,  while  the 
others  are,  useful  in  reducing  syllogisms  to  the  first 
figure  ;  for  that  is  the  special  purpose  for  which  opera- 
tions like  conversion  and  ob version  exist.     Still  there 
seems  to  be  no  more  reason  for  calling  them  infer- 
ences in  the  one  case  than  in  the  other.     Where  the 
sentences  are  equivalent,  it  is  precisely  because  they 
are  equivalent  (and  therefore  are  the  same  assertion) 
that   we  can  substitute   the  one  expression   for  the 
other.     And  the  passage  from  '  all '  to  *  some  '  is  even 
more  clearly  not  an  inference ;  for  if  we  may  not  call 
it  an  inference  where  the  datum  and  the  conclusion 
are  the  same  proposition  {ejj.  '  Some  men  are  mortal ; 
therefore    some    men    are   mortal'),    why   should    we 
call    it    so   when    the    datum    only  ditters    from   the 
conclusion  in  containing  {e.g.  'All  men  are  mortal') 
irrelevant   matter.     No  doubt    reduction    to    Fig.    I 
is  an   important  process — so  important,  indeed,  for 
explaining  the  force  of  a  given  syllogism  that  there 
is  no  need  to  recognise  the  other  figures  at  all.     All 
the  verbal  transformations  necessary  for  putting  an 
aro-ument  into  the  first  figure  may  be  made  without 
the  intermediate  step  of  putting  it  first  into  some 


I 


CH.  XI,  g  64 


KINDS  OF  ARGUMENT 


303 


other  figure.^  Formal  logicians  too  readily  forget  that 
in  order  to  get  statements  in  logical  form  at  all  a 
process  of  verbal  transformation — often  much  more 
difficult  and  risky  than  convertincr  E  or  insertin<y  a 
hyphen  between  *not'  and  the  predicate  term— has 
to  be  performed.  It  seems  somewhat  arbitrary  to 
say  that  if  I  take  the  statement '  No  news  is  good  news,' 
and  put  it  into  logical  form  as  *  Absence  of  news  is 
satisfactory,'  there  is  no  inference,  but  only  translation, 
while  if  I  then  proceed  to  alter  it  further  into  *  Absence 
of  news  is  not  unsatisfactory,'  I  have  performed  an 
inference. 

This  criticism,  however,  affects  only  the  looseness 
of  the  distinction  drawn  by  formal  logicians  between 
what  is  inference  and  what  is  not.  The  value  of  the 
rules  of  *  immediate  inference ' — or  some  of  them — 
need  not  be  in  the  least  disputed.  For  instance,  where 
S  and  P  are  two  classes,  compared  on  the  ground  of 
their  partial  or  total  inclusion  or  exclusion,  it  is  some- 
times convenient  to  have  a  handy  rule  for  avoidinty  tlie 
confusion  that  may  arise  about  the  precise  mutuality 
of  the  relation  ;  though  mutually  exclusive  classes 
present  no  conceivable  difficulty,  the  beginner  needs 
perhaps  to  be  reminded  that  if  all  the  X's  are  Y's  it 
does  not  follow  that  all  the  Y's  are  X's,  or  to  be 
reminded  that  the  proposition  *  Some  X  are  not  Y ' 
does  not  imply  '  Some  Y  are  not  X.'  Such  rules  have, 
no  doubt,  some  value,  whether  we  call  it  logical  or 
grammatical  ;    and    we    might    even    desire,    in    the 

*  For  example,  take  the  argument  that  whales  are  not  fish,  because  fish, 
as  such,  are  without  the  attribute  M  which  whales  possess.  There  is  no  need 
to  view  this  first  as  Cesare,  and  then  reduce  it  to  Celarent.  If  the  possession 
by  whales  of  the  attribute  M  is  to  be  regarded  as  a  fact  proving  that  they 
are  not  fish,  this  can  only  be  by  virtue  of  a  general  rule  that  the  attribute 
M  carries  this  consequence.  We  may  dig  this  meaning  out  of  the  sentence 
given  as  major  premiss  without  the  circuitous  process  recommended  by  the 
traditional  Logic. 


304 


USE  OF  WORDS  IN  REASONING      part  hi 


interests  of  very  young  people,  a  few  more  of  them  : 
for  instance,  that  if  X  is  to  the  right  of  Y,  then  Y  is 
to  the  left  of  X  ;  or  that  if  X  is  tlie  grandson  of  Y's 
father's  brother,  then  Y  and  X  are  first  (tousins  once 
removed.  If  it  be  an  advantage  to  Logic  to  contain 
a  large  number  of  detailed  rules  about  the  possible 
relations  between  X  and  Y,  there  are  evidently  great 
opportunities  for  advantageous  expansion. 

The  second  branch  of  inquiry  referred  to  above 
(p.  :^0l)  is,  however,  more  interesting  to  Logic — the 
question  how  far  inference  without  mediation  is 
possible,  or  whether  *  immediate  inference,'  when  it  is 
inference  at  all,  is  anything  else  than  mediate  inference 
with  the  connecting  link  passed  over  so  lightly  that 
it  escapes  notice.  If  we  share  the  modern  view  of  the 
impossibility  of  inferring  'from  particulars  to  parti- 
culars'  ;  if,  for  instance,  we  agree — as  I  do— with  Mr. 
Bosanquet  {Lixjir,  ii.  29)  that  the  (-ases  of  inference 
thus  viewed  by  Mill  may  rather  be  identified  with  the 
species  of  inference  in  which  a  confused  or  implicit 
universal  is  really  the  ground  ;  how  shall  we  conceive 
any  class  of  inference  as  inmiediate,  except  in  some 
sense  too  loose  for  anything  but  an  admittedly  care- 
less Logic?  Mr.  Bosan(|uet  (//>/>/.  20)  seems  partly 
content  and  partly  not  content  tu  use  the  name  'imme- 
diate inference'  for  such  processes  as  Recognition, 
Abstraction,  Comparison,  Identification,  and  Discrimi- 
nation. That  is  to  say,  while  calling  them  '  the  true 
immediate  inferences,'  he  seems  also  {Und.  27)  to  regard 
them  as  processes  which  are  not  strictly  independent 
of  a  universal,  but  only  of  a  universal  which  can  easily 
find  definite  expression.  When,  for  instance,  we  com- 
pare any  concrete  case  of  A  with  a  concrete  case  of  B 
and  find  them  alike,  in  what  way  does  the  process 


CH.  XI,  §  64  KINDS  OF  A  RG  UMENT  305 

differ  from  that  performed  by  Mill's  village  matron, 
who  reasons  from  the  particular  case  of  her  child 
Lucy  to  that  of  her  neighbour's  child  ?  The  notion 
of  inference  seems  to  demand  on  the  one  hand  that 
there  shall  be  difference  between  the  concrete  fact 
reasoned  from  and  the  concrete  fact  reasoned  to; 
and,  on  the  other  hand,  that  there  shall  be — 
whether  dimly  or  clearly  seen— a  universal  which 
connects  them. 

And  if  we  admit,  as  we  found  in  chap,  iv.,  that 
forward  inference  from  known  to  unknown  is  no  more 
than  the  growth  of  a  judgment,  must  we  not  also 
admit   that  there   are   always  steps  in   the  process, 
whether  easily  recognised  steps  or  not  ?     The  sudden- 
ness of  the  leap  from  one  truth  to  another,  or  from 
one  aspect  of  an  old  truth  to  another,  must  be  illusory 
and  dependent  partly  on  our  lack  of  attention  to  the 
workings  of  the  mind  that  infers.     At  any  rate,  the 
distinction  between  steps  that  are  easily  visible  and 
those  that  are  less  easily  visible  and  those  that  are 
almost  or  quite  invisible  is  plainly  too  loose  to  be  of 
much  value  for  logical  theory.     And  whether  it  can 
be  put  to  any  service  or  not,  nothing  is  gained  by 
confusing  '  immediate  inference,'   in  this  sense,  with 
translation  of  sentences  from  one  form  into  another. 
As  Logic  is  taught  in  the  textbooks,  its  only  concern 
with  immediate   inference   seems   to   lie  in  framing 
rules    for    interpreting    various    forms    of   sentence, 
partly  according  to  their  most  common  acceptation, 
and  partly  according  to  arbitrary  agreements  among 
formal   logicians — for  instance,  an   agreement   that 
'some'  shall  mean   'some   at  least,'  and  not  'some 
only,'     There  is  of  course  convenience  to  the  logician, 
as  to  other  people,  in  knowing  the  grammar  of  his 

20 


300 


USE  OF  WOPiDS  L\  UKASOMXa      vwxi  \\\ 


period  and  country,  or  the  other  conventions  which 
his  neighbours  are  likely  to  accept,  but  there  is  more 
than  mere  convenience  to  him  in  kee[)ing  in  mind 
the  limits  of  the  importance  of  these  accidental  and 


changeal)le  facts. 


PAET  IV 


SUMMARIES 


CHAPTER  XII 


THE   CAfSE   AGAINST    FORMAL    LOGIC 


8  G5. — The  Limits  of  the  Accusation 

For  the  convenience  of  readers  who  are  inclined  to 
defend  Formal  Logic,  or  at  least  to  think  that  some 
of  the  foregoing  scattered  charges  against  it  are 
exaggerated  or  unduly  pressed,  it  may  now  be  worth 
while  to  put  these  charges  together  in  summary  form, 
in  the  hope  of  guarding  still  further  against  mis- 
understandings. I  will  begin  with  a  few  disclaimers 
of  a  general  kind. 

In  the  first  place,  the  name  *  Formal  Logic '  has 
here  been  used  (pp.  7-10)  as  a  short  expression  for  '  any 
Logic  which  is  either  systematically  or  unintentionally 
more  formal  than  it  need  be.'  The  objections  are  thus 
intended  to  lie  against  contentment  with  formality 
rather  than  against  formality  per  se.  It  is  fully 
admitted  that  Logic,  like  any  other  science,  cannot 
possibly  escape  formality  altogether;  that  with  the 
best  intentions  of  judging  individual  cases  upon  their 
merits,  it  is  mere  illusion  to  suppose  that  we  can  win 
complete  freedom  from  general  rules.  It  is  fully 
admitted  that  we  cannot  move  a  step  in  any  kind  of 
thought  without  using  general  rules  (pp.  73,  86)^; 

*  As  to  the  use  of  general  rules  iu  prediction,  see  p.  24  ;  in  the  organisa- 
tion of  knowledge,  see  g  b. 


i 


310 


USE  OF  WORDS  IN  REASOMNG      part  iv 


and  that  the  only  possible  contrast  is  l)etween  accept- 
ing this  or  that  general  rule  uncritically,  and  on  the 
other  hand  using  it  with  an  eye  upon  its  faults.  The 
defects  of  Formal  Logic,  therefore,  cannot  be  remedied 
by  going  direct  to  the  opposite  extreme.  The  differ- 
ence of  method  proposed  is  not  that  between  attend- 
ing only  to  rules  and  attending  only  to  exceptions, 
but  between  avoiding  and  welcoming  the  discovery  of 
exceptions  to  the  rules  (pp.  28,  41,  193).  Recogni- 
tion of  the  defects  of  Formal  Logic  does  not  imply 
their  recognition  in  season  and  out  of  season.  A  rule 
when  its  exceptions  are  noticed  is  not  destroyed,  but 
only  established  on  a  firmer  foundation  (pp.  40,  61). 
The  defects  of  Formal  Logic  are  rendered  harmless  if 
we  hold  ourselves  ready  to  recognise  them  when 
the  fitting  occasion  comes.  Only,  I  should  maintain 
that  such  occasions  are  much  more  frequent  than 
the  existing  textbooks  ever  allow  their  readers  to 
suppose. 

In  the  second  place,  the  motives  of  the  formal 
logician  may  be  assumed  to  be  exactly  as  good  as 
those  of  his  opponent.  To  hold  the  view  that  Formal 
TiOgic  is  careless  Logic  does  not  in  the  least  involve 
the  view  that  the  writer  of  any  textbook  has  shirked 
his  work.  Indeed,  the  misdirected  labour  of  the  best 
of  these  writers,  and  of  their  unfortunate  victims  who 
use  the  books,  is  one  of  the  reasons  for  attempting 
some  reform.  And  evidently  two  at  least  of  the 
motives  most  concerned  deserve,  in  themselves, 
nothing  but  admiration — namely,  the  desire  to  get 
certainty  as  perfect  as  possible,  and  the  desire  to 
simplify  the  subject  for  teaching  purposes  by  leaving 
questions  of  detail  to  be  considered  afterwards  or 
elsewhere.     If  these  things  could  be  done  by  Formal 


CH.  XII,  .^  65  THE  CASE  AGAINST  FORMAL  LOGIC  311 

Logic,  at  a  cost  which  is  not  excessive,  then  Formal 
Logic  would  be  justified.     My  contention,  however 
(summarised  in  the  next  three  sections),  is  that  both 
the   certainty    and   the    simplification    are   in   their 
ditferent  ways  delusive ;  that  the  only  perfect  axio- 
matic certainties  of  Logic  are  empty  truisms  of  a 
practically  misleading  kind;    that  the  assumptions, 
])y  means  of  which  simplification  is  hoped  for,  lead 
to  unexpected  complication  and  confusion ;  and  that 
any  real  simplification  achieved  by  Formal  Logic  is 
ol3tained  at  excessive  cost,  since  the  practical  value 
of  Logic  is  thereby  almost  destroyed.     Logical  theory, 
thus  simplified,  is  applicable  only  to  the  flattest  and 
least  disputable  cases  of  reasoning.     Exactly  where 
Logic    is   wanted,   to    improve   upon   common -sense 
views.  Formal  Logic  breaks  down. 

And  in  the  third  place,  it  is  also  admitted  freely 
that  the  mistakes  and  omissions  of  Formal  Logic  are 
for  the  most  part  of  a  subtle,  partly  defensible  kind. 
Gross  and  downright  blunders  are  comparatively  rare. 
We  have  had  occasion,  indeed,  to  notice  one  or  two 
such,— as,  for  instance,  the  needlessly  confused  account 
of  connotation  (pp.  245-251),  or  again  the  identifica- 
tion of  the  consequent  clause  of  a  hypothetical  with 
the  hypothetical  as  a  whole  (p.  274) ;  but  most  of  the 
defects  of  Formal  Logic  are  of  another  order  altogether, 
more  insidious,  and  therefore  more  diflftcult  to  cure. 
For  centuries  great  trouble  has  been  taken  in  elaborat- 
ing the  system  within  its  self-imposed  limits;  and 
where  loose  and  careless  views  have  been  adopted  from 
common-sense,  or  cramped  and  ignorant  views  from 
early  science  and  philosophy,  it  is  often  possible  to 
find  some  excuses  for  them,  either  as  simplifications 
for  teaching  purposes,  or  on  the  ground  of  a  laudable 


I 


312 


USE  OF  WORDS  IX  EKASOXIXO 


PART  IV 


1*1 


desire  to  counteract  the  miscliievous  kinds  of  sceptical 
inquiry  (pp.  108,  109)  and  of  verbal  quibbling 
(pp.  153,  154,  176),  or  on  the  ground  of  their  adapta- 
bility to  hurried  everyday  needs  (pp.  54,  208,  216). 
Always  the  most  difficult  charge  to  bring  home  is  that 
of  excess  of  zeal  in  a  good  cause ;  and  on  the  whole 
that  is  the  chief  source  of  the  faulty  principles  and 
methods  of  Formal  Loiric. 

The  further  admission  should  perhaps  be  made  that 
some  propaedeutic   value   belongs  to  the  traditional 
system ;  but  the  question  is,  rather,  whether  a  higher 
value  of  this  kind  may  not  be  obtained  in  another 
way ;  and  some  suggestions  to  this  effect  are  made 
in  the  next  chapter.     It  is  of  course  a  commonplace  of 
the  art  of  education  that  in  order  to  teach  a  difficult 
science  it  is  often  necessary  to  tell  the  beginner  much 
that  he  will  afterwards  find  to  be  not  strictly  true ; 
that  you  must  give  him  a  rough  inexact  account  first, 
and  leave  him  to  add  the  required  corrections  later. 
But  if  we  admit — as  I  should— that  there  is  some  truth 
in  this,  still  the  interesting  question  always  remains 
how  far  exactly  the  compromise  should  be  carried, 
and  how  this  method  should  be  applied  in  matters  of 
detail  (pp.  52,  53).     Merely  because  the  general  prin- 
ciple is  admitted  we  are  not  bound  to  assume  without 
further  inquiry  that  a  particular  teaching  system — 
say   Formal   Logic — carries  it  exactly  to  the   right 
point  and  no  further,  or  even   uses  it  m   the   right 
direction.     Until  these  doubts  are  fairly  dealt  with, 
the  effective  force  of  any  such  defence  of  Formal 
Logic  seems  to  lie  chiefly  in  the  chaotic  character  of 
our  present  theories  of  education,  and  the  consequent 
difficulty  of  disproving  hasty  assertions  or  superstitious 
beliefs  as  to  the  best  methods.     Views  about  what 


CH.  XII,  §  65  THE  CASE  AGAIXST  FORMAL  LOGIC  313 

the  learner  can  or  cannot  do  are  formed  almost  as 
lightly  and  held  almost  as  obstinately  as  views  on 
the  question  what  subjects  provide  the  best  *  mental 
discipline.*  Most  of  us  are  a  little  inclined  to  believe 
that  our  ow^n  course  of  education  has  peculiar  virtue, 
— that  Greek,  or  Mathematics,  or  Natural  Science,  or 
whatever  it  may  be,  is  the  one  most  important  mental 
exercise  any  one  can  take.  When  we  can  say  nothing 
else  in  favour  of  an  educational  subject,  we  can  gener- 
ally claim  that  it  provides  the  best  possible  mental 
training.  People  may  doubt  us  or  contradict  us,  but 
no  one  can  exactly  prove  us  wrong. 

However,  in  the  particular  case  of  Formal  Logic  we 
can  go  a  little  further  than  the  mere  recognition  that 
its  educational  value  is  not  proven  ;  we  can  show  (1) 
that  its  supposed  simplifications  are  to  a  great  extent 
illusory ;  (2)  that  where  they  are  not  so  they  restrict 
the  application  of  Logic  to  insignificant  dimensions ; 
and  (3)  that  their  eflect  is  to  obstruct  as  far  as  possible 
the  improvement  of  logical  theory  in  its  attempt  to 
explain  the  difference  between  good  and  bad  reasoning. 
We  will  now  consider  each  of  these  alleged  defects 
in  the  order  given,  tracing  them  to  their  source  partly 
in  the  main  assumptions  which  (pp.  16,  17)  we  have 
taken  to  be  most  essential  to  Formal  Logic,  partly  in 
other  assumptions  which  help  to  support  these,  and 
are  in  turn  supported  by  them,  and  partly  in  certain 
negligent  habits  of  thought  and  defects  of  method 
which  are  natural  in  themselves,  and  are  also  a  natural 
outcome  of  these  restrictions  of  view.  And  we  will 
begin  with  the  least  important  of  the  three  main 
charges — the  illusoriness  of  the  simplification  which 
Logic  hopes  to  achieve  by  means  of  formality. 


314 


USE  OF  WORDS  IX  REASONING      part  iv 


5J  (ji]. — The  Simplification  Illusory 

The  simplification  attempted  by  separating  reason- 
ing process  from  subject-matter  (pp.  D-IG)  is  easily 
understood.  Since  not  even  the  most  formal  logician 
would  pretend  that  all  faulty  conclusions  are  entirely 
due  to  faults  in  the  'reasoning  process/  we  must  assume 
that  the  object  of  this  separation  is  mainly  methodical, 
the  idea  l)eing  to  attack  one  part  of  a  large  question 
at  a  time — to  clear  the  way  for  (questions  of  detail  by 
making  sure  of  questions  of  principle  first.  In  itself, 
at  any  rate,  such  an  idea  is  plainly  a  good  one,  and 
is  much  used  both  in  science  and  in  daily  life ;  the 
question  is,  what  are  its  precise  effects  in  Logic  ? 

By  restricting  attention  to  the  danger  of  *  reason - 
iiio:'  incorrectly  with  faultless  material  we  decide  to 
ignore  (if  we  can)  all  kinds  of  error  in  getting  a 
conclusion,  except  those  which  are  preventible  by 
mechanical  rules  (pp.  12,  79,  97,  126);  and  it  then 
only  remains  to  draw  up  our  rules,  and  to  practise  the 
student  in  using  theuL  This  looks  very  plain,  straight- 
forward sailing  at  first,  and  it  is  of  course  a  convenience 
to  be  able  to  say,  whenever  a  real  difficulty  is  encoun- 
tered, that  it  lies  outside  our  province.  But  if  the 
cost  of  the  simplification  is  reckoned  up,  we  find  some 
rather  startling  items  in  it,  quite  apart  from  the  further 
question  as  to  the  practical  and  theoretical  value  of 
such  a  system. 

On  the  whole,  we  have  seen  that  the  needless  com- 
plications are  mainly  caused  by  the  undue  importance 
given  to  forms  of  sentence,  and  by  the  confused 
account  of  the  technical  distinctions.  As  regards  the 
former,  this  is  necessarily  involved  in  the  conception 


CH.  xii,  ^6G  THE  CASE  AGAINST  FORMAL  LOGIC  315 

of  a  reasoning  process  distinct  from  subject-matter, 
and  is  aided  by  the  confusion  between  assertion  and 
sentence.  For  such  a  conception  requires  a  sharp 
distinction  between  a  '  piece  of  reasoning '  and  a 
*  single  proposition'  (p.  Ill);  and  this  depends  on 
our  being  able  to  distinguish  between  '  one '  proposi- 
tion and  '  more  than  one  * ;  which  is  only  possible  if 
we  mean  by  the  '  proposition '  merely  the  sentence 
(pp.  117,  143,  273,  301).  Hence  'reasoning'  opera- 
tions are  restricted  to  the  manipulation  of  ready- 
prepared  material,  such  as  sentences  in  '  logical  form,* 
and  tlius  (leductiveLogic  is  mainly  concerned  w^th  rules 
for  interpreting  sentences  (pp.  19,  259,  305).  In  the 
traditional  Logic  the  problem  is  to  regulate  the  inter- 
pretation of  pairs  of  sentences  which  have  a  term  (M) 
common  to  both,  so  as  to  combine  the  two  into  one 
(the  conclusion)  by  dropping  M  out  of  account.  But 
as  subsidiary  to  this  operation  there  are  also  a  number 
of  rules  for  interpreting  single  sentences  by  twisting 
them  into  other  equivalent  forms.  The  system  as  a 
whole  enables  to  do  by  the  help  of  rules  exactly  what 
a  machine  might  do  by  its  construction, — to  get  per- 
fectly certain  results  from  ready-prepared  material. 
The  premisses  are  put  in  at  one  end  of  the  machine, 
and  (if  it  is  controlled  so  as  to  avoid  '  undistributed 
middle  '  and  the  rest  of  the  formal  deductive  fallacies) 
the  proper  conclusion  comes  out  at  the  other  end 
triumphantly. 

Evidently,  if  rules  for  the  interpretation  of 
sentences  are  to  be  regarded  as  in  any  way  im- 
portant, this  can  only  be  through  the  assumption  that 
sentence-forms  as  such  have  a  peculiar  virtue.  Granted 
that  the  identity  of  the  sentence  with  the  assertion 
is  nowhere  put  forward  by  Formal  Logic  as  a  general 


31G 


USE  OF  WORDS  IX  EEASONIXG      paiit  iv 


If 


truth  without  exceptions,  and  tliat  in  such  a  form  it 
would  probably  be  disclaimed  even  by  those  who  define 
a  *  proposition '  as  a  sentence  indicative  and  who  yet 
make  no  express  distinction  between  propositions  and 
assertions  (p.  17  n.)\  granted  also  that  every  formal 
logician  admits  that  sentences  as  given  often  need  to  be 
re-organised  before  they  l)ecome  the  prepared  material 
required  for  applying  the  rules  of  the  Syllogism  or  of 
*  Immediate  Inference ' ;  and  that  this  ahnost  carries 
with  it  the  further  admission  that  the  question  how 
to  interpret  a  given  sentence  may  occasionally  be 
troublesome ;  still  the  point  is  that  all  ditti<ulties  of 
interpretation  except  just  those  which  the  rules  pro- 
vide for,  and  which  occur  only  after  the  'logical  form  ' 
has  been  somehow  arrived  at,  are  treated  bv  Formal 
Logic  as  lightly  as  possible  (pp.  19,  20,  2G0,  283). 
Tartly  by  fixing  the  student's  attention  on  the  simplest 
kind  of  predicative  sentences,  like  *  Socrates  is  mortal.' 
partly  by  saying  very  little  about  the  process  of  trans- 
lation into  logical  form,  the  impression  given  by  the 
textbooks  is  that  difficulties  in  getting  satisfactory 
material  for  Formal  Logic  to  work  upon  are  not  on 
the  whole  of  much  importance.  Such  difficulties, 
though  their  existence  is  never  exactly  denied,  are 
treated  not  as  directly  aflecting  the  main  body  of 
syllogistic  doctrine,  l)ut  rather  as  small  and  excep- 
tional matters  of  detail  which  can  be  considered 
later  by  those  who  think  it  worth  while.  And  the 
habitual  readiness  of  popular  thought  to  postpone 
the  consideration  of  difficulties  till  another  time  here 
strengthens  the  hand  of  Formal  Loo-ic. 

This  tendency  to  minimise  and  neglect  difficulties 
of  interpretation  has  far-reaching  evil  consequences. 
One  of  its  minor  effects  is  to  complicate  the  abstract 


CH.  xu,  §  (S(j  THE  CASE  AGAINST  FORMAL  LOGIC  317 

syllogistic  doctrine  needlessly  (p.  62  n.)  When  the  pro- 
cess of  translating  sentences  into  logical  form  is  given 
its  due  importance  we  begin  to  find  that  there  is  no 
good  reason  for  considering  that  process  ended  with 
the  arrival  at  the  mere  form  '  S  is  P,'  but  that  what 
is  really  wanted  (for  clearing  up  the  general  view  of 
the  Syllogism)  is  the  translation  of  given  sentences 
straight  into  premisses  in  the  first  figure  (pp.  278,  297, 
and  5J  64), — an  operation  which  would  add  compara- 
tively little  to  the  initial  difficulty  of  getting  from 
colloquial  or  literary  form  to  the  typical  predicative 
form,  and  would  greatly  simplify  the  rules  for  avoidinc^ 
syllogistic  fallacy.  Moreover,  the  rules  of  Immediate 
Inference — so  far  as  they  are  needed  at  all — would  then 
be  used  only  in  the  case  where  the  sentence  as  given 
is  already  in  predicative  form  but  is  not  yet  formally 
brought  into  the  required  relation  to  the  other  premiss. 
And  since  sentences  in  the  simplest  predicative  form  are 
not  very  often  met  with  outside  the  textbooks,  the  use 
of  the  rules  of  Immediate  Inference  would  be  found 
much  more  restricted  than  the  textbooks  assume  it 
to  be.  As  far  as  their  practical  value  goes  they  are  both 
incomplete  and  in  some  cases  (p.  303)  rather  trivial. 
For  instance,  knowledge  of  the  mutuality  of  class- 
relations  (conversion)  is  only  a  small  part  of  our 
knowledge  of  the  mutuality  of  relations  in  general, 
and  other  parts  of  this  wider  knowledge  are  equally 
wanted  for  translating  sentences  into  logical  form ; 
while  knowledge  of  the  fact  that  two  negatives  make 
an  affirmative  (obversion)  is  a  mental  equipment 
so  elementary  that  a  person  who  did  not  already 
possess  it  would  hardly  know  enough  to  begin  the 
study  of  Logic  at  all. 

Further  unnecessary  complications  of  logical  doc- 


ii 


1 

If 


M 


318 


USE  OF  WOIWS  IN  liEASOXING      paiit  iv 


11 


trine,  which  we  have  found  to  be  due  to  the  confusion 
between  assertion  and  sentence,  are  the  distinctions 

(1)  between  the  athrmative  and  negative  copuhi,  and 

(2)  between  categorical  and  other  kinds  of  Syllogism. 
As  resards  the  former  it  is  evident  that  so  far  as  the 
quality  of  the  assertion  goes — assertion  as  distinct 
from  sentence — there  is  no  difference  between  A  and  E. 
or  between  I  and  0  (§  58).  An  E  or  an  O  proposition 
is  not,  as  such,  any  less  affirmative — any  cheaper  or 
more  cautious — than  an  A  or  an  I  proposition  respec- 
tively. Why  then  distinguish  E  and  0  as  negative  ; 
why,  in  putting  sentences  into  logical  form,  take  any 
more  notice  of  the  accidental  position  of  the  negative 
siirn  than  we  take,  for  instance,  of  the  order  of  the 
words  in  *  Great  is  Diana '  ?  The  effect  of  doing  so 
is  to  doul)le  the  number  of  typical  forms  of  categorical 
syllogism  recjuired. 

Then  as  retjards  the  distinction  between  categorical 
and  other  syllogisms,  we  found  in  §  63  that  this 
unnecessary  complication  was  due  to  the  formal  dis- 
tinction between  categorical  and  hypothetical  pro- 
positions ;  which,  when  applied  (according  to  the 
habit  of  Formal  Logic)  to  propositions  regarded  as 
separate  entities  independent  of  their  special  context 
in  a  syllogism,  has  no  basis  outside  the  use  to  which 
sentences  of  this  or  that  verbal  form  are  commonly 
put, — their  average  function, as  we  may  call  it  (p.  275). 
So  that,  as  soon  as  it  is  recognised  that  a  hypothetical 
or  conditional  assertion  is  not  constituted  by  the  pre- 
sence in  the  sentence  of  words  like  *if'  or  *  when,'  or 
by  any  other  purely  formal  details  of  structure,  but 
solely  by  its  temporary  function  as  major  premiss, 
then  the  double  set  of  syllogistic  rules  serves  only 
to  darken  and  confuse  logical  theory.     The  essential 


CH.  XII,  §66  TffF  CASE  AGAINST  FORMAL  LOGIC  319 

requisites  of  the  abstract  syllogistic  framework  are 
partly  hidden  under  trivial  and  irrelevant  details  of 
difl'erence  in  the  mere  form  of  expression. 

In  the  next  place.  Formal  Logic's  systematic 
neglect  of  context  (§  52),  which  is  closely  related  to  the 
confusion  between  assertion  and  sentence,  works  against 
simplicity  and  clearness  chiefly  through  the  defects 
of  the  technical  distinctions  between  kinds  of  term 
and  of  proposition, — tlirough  the  confused  account 
the  textbooks  are  compelled  to  give  of  the  'logical 
character '  of  this  or  that  word  or  sentence.  How  can 
there  be  any  real  simplification  of  doctrine  where  the 
technicalities  whose  function  is  to  express  the  doc- 
trines are  not  only  inexact  and  self-contradictory  but 
are  prevented  by  the  very  conditions  of  their  exist- 
ence from  ever  emerging  into  clearness?  Our  con- 
tention is  that  in  this  respect  the  whole  foundation 
of  Formal  Logic  is  unsound ;  that  no  amount  of  care 
and  ingenuity  spent — as  Dr.  Keynes  and  others  have 
freely  spent  it  —  in  patching  up  defects  in  these 
technicalities,  without  a  radical  change  in  the  point 
of  view,  can  ever  succeed  in  reaching  the  source  of 
the  evil. 

An  inevitable  result  of  neglecting  context  in 
determining  logical  character  is  to  make  the  distinc- 
tions loose,  like  those  of  Grammar  (p.  243).  We 
noticed  just  now  the  confused  account  thus  given  of 
the  distinction  between  affirmative  and  negative 
propositions,  and  between  categoricals  and  hypo- 
thetical ;  of  distinctions  among  kinds  of  term  the 
two  that  do  most  to  perplex  logical  doctrine  are  that 
between  abstract  and  concrete  names  (§  56),  and  that 
between  general  names  and  all  others  (§  54).  The  con- 
ception of  abstract  names   is,   we  found,   a  merely 


i 


20 


USE  OF  WORDS  IN  REASONING      part  iv 


grammatical  one,  and  any  attempt  to  use  it  with 
the  definiteness  required  for  logical  technicalities 
inevitably  causes  confusion  ;  as  may  be  seen,  for  ex- 
ample, from  the  empty  and  wearisome  discussions  as 
to  whether  abstract  names  are  general  or  singular,  and 
whether  they  are  connotative  or  not  (p.  257).  And 
in  reofard  to  general  names  it  is  clear  that  to  define 
them  as  those  which  are  *  capable  *  of  such-and-such 
uses  is  to  ignore  the  fact  that  any  name  is  capable  of 
whatever  use  we  choose  to  put  it  to  (pp.  242,  251). 
No  doubt,  however,  *  customarily  capable '  is  what 
Formal  Logic  really  intends ;  it  intends  to  draw  the 
distinction  between  those  names  which  in  their  average 
context  are  class-names  and  those  which  in  their 
average  context  are  not  so.  This  again  is  legitimate 
enough  as  a  grammatical  distinction,  confessedly 
loose ;  but  as  a  logical  one  —  an  instrument  for 
expressing  logical  doctrines — it  breaks  down  just  at 
the  point  where  firmness  is  most  required.  Leaving 
out  of  account  the  more  serious  results  of  this  loose- 
ness of  technicality,  we  have  at  present  only  to 
notice  that  the  simplicity  gained  by  having  a 
terminology  in  this  condition  is  largely  delusive. 
So  long  as  the  main  source  of  difficulties  in  applying 
the  technical  terms  is  ignored  there  can  be  no  general 
agreement  among  logicians  as  to  their  precise  applica- 
tion ;  but  each  will  attempt  to  meet  those  particular 
difficulties  which  happen  to  have  occurred  to  him, 
and  the  result  must  be  divided  counsels  among  the 
teachers,  and  perplexity  for  the  student. 

Along  with  neglect  of  context  we  should  reckon 
also  as  an  inffuence  tending  to  complicate  Formal 
Logic  needlessly  the  habit  of  regarding  technicalities 
not  as  instruments  of  precise  expression  but  rather  as 


CH.  XII,  .^67  THE  CASE  AGAINST  FORMAL  LOGIC  321 

foreign  words  requiring  translation  (pp.  42  ff*.).  Perhaps 
an  excuse  may  be  found  in  the  lact,  just  noticed,  that 
the  traditional  account  of  the  technicalities  prevents 
their  actually  being  instruments  of  precise  expression  ; 
but  a  result  of  this  habit  is  that  little  or  no  distinction 
is  made  between  useful  technicalities  and  others  (p.  52), 
and  that  consequently  any  technicality  which  at  any 
period  in  the  long  history  of  Logic  has  found  a  foot- 
ing in  the  system  has  a  tendency  to  stay  there  after 
its   value  is  gone.      Many,  no  doubt,  are  perfectly 
harmless, — like  that  between  categorematic  and  syn- 
categorematic  words,  or  between  the  Goclenian  and 
other  kinds  of  Sorites  ;  others  again  are  now  harmless 
because  they  are  seldom  or  never  referred  to  when 
once  their  definition  has  been  given, — e.g.  the  dis- 
tinction   between    positive    and    negative    terms,    or 
between    absolute    and    relative   terms,    or   between 
collective   terms   and   those   contrasted   with    them. 
All    that   we   need  here  notice  is  that  retention  of 
such  technicalities,  though  it  may  otherwise  do  no 
great    harm,    is    a    departure    from    that    ideal    of 
snnplicity   for   the  sake  of  which  so  many  of  the 
sacrifices  of  Formal  Logic  are  presumaljly  made.     It 
has,  too,  the  further  result  of  encouraging  common 
sense  to  think  the  study  of  Logic  trivial. 

§  67.  —The  Doctrines  Unimportant 

But  the  failure  of  Formal  Logic  to  achieve  the 
<lesired  simplicity  is  the  least  important  of  the 
objections  here  brought  against  the  system,  and 
perhaps  we  need  not  discuss  it  further.  Let  us  look 
now  at  the  effect  of  its  real  simplifications,  and  first 
at  their  effect   in   making  logical   doctrines   almost 

21 


^ 


322  USE  OF  WORDS  IN  REASONING      rAiiTiv 

useless  for  application  in  any  case  where  a  piece  of 
plausible  reasoning  is  called  in  question. 

The  separation  of  reasoning  process  from  subject- 
matter,  though  it  involves  the  confusion  of  sentence 
with  assertion  and  thus  leads  to  the  complications 
noticed  above,  is  in  itself  a  real  simplification  of  the 
problem    of    Logic,   just    as    we    may    simplify    any 
difficult   subject    by   ignoring   its   worst   difficulties. 
When    this    is  done,   however,   the   question   always 
remains    whether   it    was    worth   doing.      If   formal 
logicians   have  ever   faced    this  question   they   have 
not  taken   their   readers  into  their  confidence  as  to 
the   way   in    which   they   would   deal   with   it;  they 
appear  rather  to  assume  the  value  of  their  crippled 
science  without  inquiry,  and  almost  to  glory  in  its 
limitations.      When,   for   instance,   as   in   Whateley's 
Essmj  on  the   Province  of  Rensoniiaj,  the  doubt  is 
referred  to  at  all,  the  line  of  defence  adopted  is  an 
indignant  remonstrance  against  the  mere  suggestion 
of   it.     **  Why  blame   us,"   they  seem   to  be  saying, 
*'  for  not  doing  things  which  we  have  never  under- 
taken to  do?"     Formal   Logic  has  never  pretended, 
these  apologists  say,  to  take  account  of  context,  or 
to  discuss  the  relation  between  thought  and  language, 
or  to  entertain  questions  about  the  subject-matter  of 
reasoning.      It   recognises,   indeed,   the   existence  of 
indefinite  words  and  ambiguous  assertions,  but  dis- 
misses them  as  lying  outside  its  province ;  which  is, 
to    trace    the    relation    between   propositions    whose 
meaning  is  taken  as  clearly  understood. 

Our  answer  to  such  a  defence  is,  in  the  first  place, 
that  this  is  at  most  the  professed  intention  or  aim  of 
Formal  Logic;  that  all  existing  systems  of  Logic 
(except  those  which  are  purely  symbolic)  do  in  fact 


CH.  XII,  i^  67  THE  CASE  AGAINST  FORMAL  LOGIC  323 

depart  to  some  extent  from  so  simple  a  purpose,  and 
venture  occasionally  on  more  interesting  and  more 
difficult  ground.^  And  in  the  second  place,  that  so 
far  as  they  do  not  '  undertake '  this  venture,  that  is 
precisely  the  fault  we  find  with  them.  Contentment 
with  formality  can  go  no  further.  It  is  a  strange 
defence  against  a  charge,  to  plead  that  the  act  was 
done  with  deliberate  intention.  If  the  intention 
could  be  justified,  of  course,  that  would  be  a  relevant 
reply. 

Then  can  it  be  justified  ?  One  reason  for  doubt- 
ing this  is  that  the  theory  of  good  and  bad  reasoning 
readied  by  Formal  Logic  differs  scarcely  at  all  from 
tliat  contentedly  held  by  common  sense,  except  in 
t  he  false  appearance — due  to  its  elaborate  terminology 
— of  being  scientific." 

Indeed  the  difference  is  rather  to  the  disadvantage 
(►f  Formal  Logic,  since  the  latter,  besides  being  equally 
ready  to  accept  thin  wordy  arguments  as  valid,  is 
less  able  to  transcend  its  own  formalities.  The 
special  defect  of  the  formal  view  of  the  goodness  or 
badness  of  a  piece  of  reasoning  is  that  it  systematic- 
ally leaves  out  of  account,  both  in  deduction  and  in 
induction,  the  very  thing  that  most  affects  the 
character  of  any  actual  judgment  that  is  likely  to 
win  credence  (pp.  66,  93).     In  consequence  of  this 

*  Of  course  no  inductive  Logic,  however  formal,  can  be  content  to  ignore 
all  (lueations  about  causation.  But  even  in  deductive  Logic  a  similar  attrac- 
tion is  inevitably  felt  towards  (questions  about  classification  and  definition. 
As  Dr.  Keynes  says  {Formal  Logic,  p.  3),  "the  principles  by  which  valid 
thought  is  regulated,  and  more  esjKJcially  the  application  of  those  principles, 
cannot  be  adoipiately  discussed  unless  some  account  is  taken  of  the  way  in 
which  [language]  actually  j^erforms  its  functions."  Evidently  this  lets  in  the 
thin  end  of  a  considerable  wedge. 

2  The  fundamental  likeness  is  in  the  desire  to  preserve  broad  rules,  un- 
hampered by  troublesome  knowledge  of  their  exceptions  (pp.  46,  51). 
Many  of  the  cases  in  which  Formal  Logic  encourages  loose  popular  views,  or 
distinctions,  seem  traceable  to  this  desire  ;  for  instance,  those  that  were 
noticed  in  chapters  vi.  and  vii. 


324  USE  OF  WORDS  IN  REASONING       partiv 

omission  it  restricts  the  application  of  Logic  to  exces- 
sively simple  kinds  of  error  in  reasoning,— easily  pre- 
ventable mistakes  like  those  we  make  in  adding   a 
column  of  figures,  as  opposed  to  the  kind  of  mistake 
which  has  vitality  (pp.  74,  83, 12G-128,  288).     Deduc- 
tive Logic  so  treated  becomes,  as  we  noticed  just  now 
(pp.  315,  319),  little  more  than  a  department  of  Gram- 
mar, with  a  false  importance    given    to    meclianii^al 
rules  for  interpreting  sentences  ;  and  though  inductive 
Logic  is  usually  a  little  less  marred  by  formality,  still 
even  there  the  chief  source  of  error  is  kept  considerably 
out  of  focus.     Something,  but  not  enough,  is  generally 
said  about  the  ditiiculty  of  being  sure  that  only  one 
circumstance  has  varied  (pp.  94  if.,  107);  and  it  is 
said  rather  by  way  of  afterthought  than  as  part  of  the 
main  doctrine.     As  we  saw  (pp.   93,  127),  the  chief 
source  of  faulty  induction  is  to  be  found  not  in  igno- 
rance of  the  abstract  canons,  but  in  mistaken  applica- 
tions of  them  owing  to  the  way  in  which  the  defects 

of  t^eneral  languac^re  have  helped  to  obscure  the  nature 

&  111 

of  the  fixcts  on  which  the  induction  is  based  ;  so  that 

formality  in  induction  is  ec^uivalent  to  empiricism,  or 
to  the  acceptance  of  facts  as  such-and-such  facts  with- 
out sutKcient    analysis    (pp.   96-99).       Similarly   the 
chief  source  of  faulty  deduction  is  lu  be  found  not  in 
ignorance  of  any  syllogistic  rules  (p.  83),  but  in  mis- 
taken applications  of  them  through  unnoticed  defects 
in    the   name    M;    which    again    implies  insutticient 
analysis  of  the  facts  described  (pp.  66,  69,  75).     And 
we  saw  that  ambiguous  middle  is  a  serious  danger  in 
syllogising  just  in  so  far  as  the  ambiguity  is  well  con- 
cealed ;  so  that  any  influence  whidi— like  readiness 
to  ignore  difticulties  of  interpretation  -tends  to  leave 
the  subtler  ambiguities  out  of  account,  tends  also  to 


(  H.  xn,  i<  67  THE  CASE  AGAINST  FORMAL  LOGIC  325 

restrict  our  power  of  recognising  errors  of  reasoning  to 
those  which  are  the  reverse  of  serious. 

Taking  as  a  whole  the  theory  of  the  difference 
between  good  and  bad  reasoning,  we  have  found  that 
the  more  formal  it  is  made  the  more  it  tends  to  neglect 
(1)  the  danger  of  ambiguity  in  all  reasoning,  and  (2) 
the  dependence  of  our  causal  interpretation  of  observed 
fact  upon  the  extent  of  our  previous  knowledge.  We 
may  now  notice  more  exactly  how  these  two  defects 
ill  theory  are  chiefly  encouraged  to  persist,  and  also 
what  is  their  practical  outcome. 

First,  then,  the  very  nature  of  ambiguity  is  mis- 
conceived by  Formal  Logic,  chiefly  in  consequence  of 
some  of  the  assumptions  which  are  inherited  from 
earlier  times  or  adopted  too  easily  from  common 
sense.  The  old  abstract  distinction  between  uni- 
vocal  and  equivocal  terms  (p.  182),  even  when  its 
looseness  in  application  is  to  some  extent  recognised, 
still  encourages  the  supposition  that  ambiguity  is 
something  which  attaches  to  a  word  isolated  from  its 
particular  context,  instead  of  to  an  assertion  in  which 
the  doubtful  word  occurs(§  43);  and  this  view  supports 
and  is  supported  by  the  common  confusion  between 
ambiguity  and  indefiniteness  (§§  40,  42).  The  latter 
confusion  again  involves  the  loose  assumption  that  it 
is  only  the  degree  of  '  indefiniteness  or  ambiguity ' 
that  matters,  though  no  test  of  the  degree  is  available 
except  just  that  quality  (importance)  w^hich  the  degree 
is  supposed  to  indicate  (§  41).  Quite  apart  from 
its  defect  of  question-begging,  such  a  view  hinders 
our  recognition  that  all  descriptive  words,  as  such,  are 
indefinite  and  therefore  liable  to  become  ambiguous 
(pp.  175, 176) ;  it  tends  to  encourage  the  false  popular 
belief   that   some   words   are   perfectly  safe   against 


#1 


326  USE  OF  WORDS  L\  REASONING       part  iv 

ambiguity,  and  that  the  type  of  an  *  ambiguous 
word '  is  a  word  which  lends  itself  to  the  making  of 
puns,  instead  of  a  word  whii^h  while  apparently  simple 
in  meaning  has  actually  destroyed  the  meaning  of  a 
particular  assertion  (pp.  181,  184).  To  (connect  the 
notion  of  *  ambiguity  '  specially  with  the  former  kind 
of  words  is  to  restrict  attention  to  that  kind  of  in- 
detiniteness  which  has  least  effective  misleading  power. 
And  when  this  is  done,  what  practical  value  can  we 
expect  from  the  complacently  stated  rule  that  '*  a 
middle  term  must  not  be  ambiguous "  i  Almost  as 
well  mif^ht  we  tell  the  student  that  if  a  syllogism 
avoids  all  fallacy  the  conclusion  will  be  correct. 

A  further  inHuence  tending  in  the  same  direction 
is  the  survival  in  Formal  Logic  of  (pertain  traces  of  the 
ancient  conception  of  the  nature  of  classes  (§§  ;3:^  36). 
How  much  of  this  mutually  remains,  in  our  times,  it  is 
difficult  to  say ;  the  mere  fact  that  some  of  the  text- 
books ffive  an  account  of  the  "Five  Predicables"  is 
not  by  itself  conclusive  evidence  of  the  survival, 
since  four  of  i\\Qm-~germs,  species,  difference,  and 
accident — can  be  transformed  and  accommodated  to 
the  modern  view  without  much  difficulty ;  and  the 
scholastic  doctrine  of  them,  and  of  propriuw,  may 
(like  so  much  else  contained  in  the  textV)ooks)  be 
merely  intended  as  matter  to  be  learnt  by  heart  and 
afterwards  dispensed  with.  The  distinction  between 
essential  and  accidental  propositions,  however  (§  59), 
is  so  important  that  any  neglect  of  its  difficulties 
of  application  seems  to  indicate  a  belief  that  class- 
names  have  some  one  *  correct '  meaning  which  bars  the 
way  to  any  more  elastic  use  of  them  (pp.  152,  1 58-162). 
And,  as  we  have  seen,  these  difficulties  receive,  as  a  rule, 
scarcely   any   attention.      Then,  again,  a  clear  view 


CH.  xn,  ^  67  THE  CASE  AGAINST  FORMAL  LOGIC  327 

of  the  nature  of  ambiguity  requires  a  clear  view  of 
difficulties  of  interpretation  generally;  and  this  (as 
we  noticed  just  now,  in  §  ^iS)  is  directly  discouraged 
by  the  whole  method  and  system  of  Formal  Logic. 

The  assumption  that  difficulties  of  interpretation 
may  be  almost  neglected  tends  not  only — as  we  saw 
-to    cause    unnecessary   complication,   ))ut    also    to 
restrict  attention  to  unimportant  matters.      Formal 
Logic  pays  so  much  attention  to  the  mere  machinery 
of  inference  that    it  has   little  left   for   the  mental 
operations  which  are  needed  l)efore  the  material  can 
be  fed  into  the  machine  (pp.  260,  303).      And  it  is 
not  only  the  doctrine  of  the  syllogism  which  is  thus 
crippled,  but  exactly  the  same  procedure  is  followed 
when  tlie  formal  logician  turns  his  attention  to  the 
causal  interpretation  of  observed  facts  by  means  of 
'  inductive  methods/      Under  his  treatment  these  also 
(p.  1)7)  become  machinery  as  contrasted  with  thought. 
The   leading   idea  of  inductive  Logic,  as  taught  on 
the  lines  of  Mill,  seems  to  be  to  exhibit  the  frame- 
work of  all  reasoning  from  observed  event  to  causal 
explanation,—  the  framework  of  good  and  bad  reason- 
ing alike, — and  to  put  into  language  the  ideal  which 
every  one  who  has  got  beyond  the  most  primitive  or 
careless    attempts    at    causal    explanation    has    long 
instinctively  followed.     Our  effective  knowledge  of 
the    difference    between    good    and    bad    inductive 
reasoning  depends  not  on   mere  recognition   of  this 
ideal,  but  also  (and  specially)  on  knowledge  of  the 
actual  difficulties  in  reaching  it.     In  the  formal  treat- 
ment of  Induction,  the   excellence  of  the  Method  of 
Difference   is   supposed    to   inhere   somehow^   in  the 
lilethod   itself  (pp.    92-96),  instead  of   in  the  care 
and  knowledge  with  which  we  have  previously  pre- 


328 


USE  OF  WORDS  IN  REASONING       pakt  iv 


pared  the  material  to  which  we   apply   it.     True  as 
it  is  that  inductive  Logic  can  never  pretend  to  lay 
down  general  rules  as  to  which  concrete  circumstances 
may  safely  be  taken  as  single  and  which  may  not,  that 
is  scarcely  a  reason  for  overlooking  the  difficulty.      It 
is  not  more  rules  that  are  wanted,  but  a  more  intelli- 
gent   recognition   of   the    defect    to   which    rules    as 
such   are   liable.       Instead   of  putting   forward   only 
examples  where  we  have  every  reason  at  present  to 
suppose    the   causal    interpretation    sound,   inductive 
Logic  should  dwell  upon  the  examples  which  can  now 
be  seen  as  plausible  but  misleading,     cases  where  one 
generation,  or  one  scientific  man,  has  taken  perhaps 
the  utmost  available  care   to  apply  the  Method   of 
I)ifl"erence  and  yet  the  next  generation  has  discovered 
the  complexity  of  some  circumstance  which  was  for- 
merly supposed  to  l)e  single,  for  upon  that  kind  of  dis- 
covery progress  in  our  interpretation  of  Nature  chiefly 
depends  ;  and  the  quality,  good  or  l)ad,  of  any  piece 
of  such   reasoning  is  determined  (care  taken   being 
equal)   entirely  l)y   the   previous   knowledge  we  can 
bring  to  bear  upon  our  observation  of  the  facts  (p.  98). 
To  concentrate  attention  on  the  process  as  contrasted 
with  the  preparation  of  the  material,  is  to  imagine  that 
each  act  of  induction   is  complete  in  itself,  without 
roots  in  the  past,  or  need  of  revision   in  tlie  future. 
Thus  the  more  formal  we  allow  our  view  of  induction 
to  be,  the  less  able  are  we  to  see  that  our  conception 
of  any  fact,   and    therefore    of   its    consequences,    is 
always  formed  under  the  direction   of  our  previous 
knowledge  of  the  laws   and  facts  of  Nature  ;  which 
knowledge  is  what  selects  for  us  (well  or  badly)  the 
important   or  relevant  details  in  any  fact,  as   those 
from  which  it  is  to  be  named.     And  though  Loijic 


C!i.  XII,  i<  67  THE  CASE  AGAINST  FORMAL  LOGIC  329 

cannot  undertake  to  guarantee  the  soundness  of 
our  previous  knowledge,  it  can  at  least  point  out 
the  efiect  of  language  in  giving  a  false  security, 
and  so  set  us  on  the  track  of  discovering  weak 
places  (p.  96) ;  it  can  help  us  to  remember — what 
Formal  Logic  is  everywhere  doing  its  best  to  hide 
from  us — the  necessary  imperfections  of  any  piece  of 
verbal  description.  Instead  of  putting  forward  the 
syllogistic  form,  or  the  form  of  the  Method  of 
Difference,  as  the  type  of  valid  inference,  it  may  use 
these  forms  for  calling  attention  to  the  weak  places  of 
every  argument, — the  possible  duplicity  of  a  statement 
of  fact  which  looks  sufficiently  simple. 

In  these  directions  and  to  this  extent,  Formal 
Logic  may  certainly  be  said  to  simplify  the  problem 
as  to  the  difference  between  good  and  bad  reasoning, 
— just  as  we  may  always  simplify  any  problem  by 
declining  to  take  the  whole  of  it  into  account.  The 
defensibility  of  this  practice  depends  on  the  purpose 
in  view.  A  great  deal  of  detail  may,  for  instance,  be 
neglected  in  certain  astronomical  calculations  without 
importantly  affecting  the  result ;  the  motion  of  the 
*  lixed '  stars  may  be  overlooked,  and  bodies  which  are 
not  rigid  may  be  taken  as  rigid,  or  surfaces  which  are 
irregular  taken  as  perfectly  smooth.  It  is  not  there- 
fore on  the  ground  of  mere  general  principle  that  this 
procedure  can  be  held  to  interfere  with  the  value  of 
Logic  ;  we  must  ask  more  exactly  how  it  affects  the 
results  of  the  special  science. 

And  here  the  essence  of  our  objection  is  that 
Formal  Logic  ceases  to  operate  just  at  the  point 
where  Logic — as  distinct  from  mere  common  sense 
and  from  Grammar — should  begin  ;  or  at  any  rate  so 
near  that  point  that  the  slight  advantage  won  is  not 


330 


USE  OF   WOEDS  IX  REASONING      i'AKT  iv 


worth   the  price  paid   in   learning  the  confused  and 
over -abundant  technicalities.      It  follows  of  course 
from  our  whole  conception  of  Logic  as  a  progressive 
and  improvable  science  that  all  expressions  referring 
to   a  'point'  at   which  a  scientific  Logic  begins  are 
inevitably    loose     and    approximate.       Since    Logic 
originates  in  common  sense,  and  since  it  never  ceases 
to  improve  upon  its  own  earlier  results,  there  can  be  no 
sharp  opposition — except  what  is  quite  artificial  and 
arbitrary — between'  Logic*  and  our  less  elaborate  views 
about  reasoning  (pp.  39-41).      It  is  not  true  that  the 
latter  are  entirely  uncritical,  nor  that  that  which  Logic 
criticises  can  never  itself  deserve  the  name  of  Logic. 
On  this  account  it  would  be  too  much  to  say  that 
Formal  Lo^ic  has  no  value.     But  that  the  tendency 
of  contentment  with  formality  must  be  towards  con- 
tentment with  inefficient  discrimination  between  good 
and  bad  arguments  we  can  find  no  room  for  doubting. 
What  can  be  expected  from  a  system  which  does  all  it 
can  to  neglect  those  difficulties  of  interpretation,  and 
those  defects  of  language,  to  which  most  of  our  lasting 
differences  of  opinion  are  due ;  and  which  does  all  it 
can    to  make    mechanical    rules    take    the    place    of 
thought  ? 

§  68. — The  Obstruction  to  Progress 

The  desire  for  simplification  is  not  the  only  motive 
which  is  characteristic  of  Formal  Logic,  nor  even 
perhaps  the  one  which  it  regards  as  the  best.  The 
separation  of  reasoning  process  from  subject-matter, 
and  the  other  assumptions  which  co-operate  with  this 
in  building  up  the  traditional  system  would  probably 
not  be  regarded  by  their  staunchest  adherents  exactly 


CH.  xn,  §  68  THE  CASE  AGAINST  FOEMAL  LOGIC  331 

as  scientific  principles.  If  defended  at  all,  they  can 
only  be  defended  as  expedients,  not  as  having  an 
independent  philosophical  value  of  their  own.  Very 
different,  however,  is  the  attempt  of  Formal  Logic  to 
base  itself  on  axiomatic  certainties  like  the  Laws  of 
Thought  and  the  Law  of  Causation ;  an  attempt 
which,  while  perfectly  consistent  with  the  general 
plan  of  ignoring  difficulties  and  appealing  to  common 
sense,  makes  also  a  loftier  kind  of  pretension. 

As  we  noticed  in  chapter  i.,  there  is  a  deep-seated 
difference  of  opinion  about  the  nature  of  a  *  scientific 
foundation  '  for  Logic  ;  a  difference  corresponding  to 
that  between  the  older  and  the  newer  view  of  the  task 
of  science  generally — between  the  ideal  of  '  reaching 
certainty'  and  that  of  gradually  improving  a  system  of 
knowledge  which  ever  remains  improvable  (pp.  28-30, 
99,227).  Formal  Logic  holds  that  in  so  far  as  Logic  can 
be  based  upon  *  undeniable  truths'  it  becomes  a  science, 
as  contrasted  with  a  chaotic  collection  of  half-formed 
opinions.  The  reason  of  this  attitude  is  not  to  be 
found,  I  think,  in  anything  worse  than  a  survival  of 
old  notions  of  the  nature  of  science.  It  seems  to  be 
chiefly  due  to  the  idea  that  mathematical  demonstra- 
tion is  the  type  of  all  proof  In  saying  this,  it  is  not 
intended  to  imply  that  the  formal  logician  necessarily 
regards  Logic  as  a  branch  of  Mathematics ;  but  only 
that  in  trying  to  find  a  firm  foundation  for  logical 
doctrines,  his  aim  is,  like  that  of  the  mathematician, 
to  trace  them  back  to  *  self-evident  truths  '  as  distinct 
from  *  admitted  truths  '  —  truths  which  may  or  may 
not  later  turn  out  to  have  been  too  hastily  admitted. 
This  was  a  natural  aim  enough  before  the  fundamental 
uncertainty  of  scientific  doctrines  had  come  clearly 
into  view.     The  prevailing  assumption,  dow^n  at  least 


332 


USE  OF  WORDS  IN  REASONING       part  iv 


to  Cartesian  times,  was  that  there  is  no  conceivable 
middle  ground  between  a  system  of  truth  built  upon 
undeniable  axioms,  and  on  the  other  hand  perfect 
anarchy.  The  notion  of  making  the  best  of  provi- 
sional truths,  and  at  the  same  time  regarding  them  as 
improvable,  does  not  easily  flourish  in  the  days  when 
a  man  may  be  burnt  at  the  stake  for  incjuiring  into 
the  truth  or  meaning  of  a  formula. 

The  view  most  strongly  opposed  to  this — the  view 
here  taken  throughout — is  extremely  liable  to  mis- 
interpretation, in  several  ways  which  it  may  be  well 
to  notice.  In  the  first  place  it  must  not  be  supposed 
that  we  seek  to  dispute  the  axiom  that  *  real  A  is  real 
A,*  or  any  other  of  the  undeniable  statements  referred 
to  (pp.  21,  32).  If  we  could  intelligibly  dispute  them 
they  would  deserve  far  more  consideration.  Nor  do 
we  make  any  great  point  of  complaining  that  because 
they  are  '  necessary  truths '  their  statement  is 
unnecessary  ;  for  the  time  they  take  to  enunciate, 
or  the  space  they  fill  on  a  page,  is  itself  scarcely 
worth  mentioning.  If  they  were  harmless  as  well 
as  necessary  (pp.  36-39)  no  one  would  seriously 
grudge  them  a  place  in  the  books,  since  few  books 
succeed  in  wholly  avoiding  irrelevant  flourishes. 
And  it  is  perhaps  needless  to  say  that  we  must  not 
be  credited  with  any  such  view  as  that  knowledge  is 
more  scientific  in  proportion  to  the  amount  of  error  it 
contains,  nor  again  that  a  (*haotic  absence  of  doctrine 
is  in  itself  a  better  thing  than  an  orderly  array  of 
truth.  Our  objection  involves  none  of  these  absurd 
positions  ;  its  basis  is  of  another  kind  altogether. 

The  harm  done  by  the  axioms  does  not  consist  in 
their  being  called  the  foundation  of  Logic,  but  in  their 
being  considered  a  firm  and  satisfactory  foundation. 


OH.  xn,  §  68  THE  CASE  AGAINST  FORMAL  LOGIC  333 

or  a  means  of  justifying  any  logical  doctrine  which 
can  be  deduced  from  them  (pp.  25-27, 161).  It  would 
be  less  misleading  to  call  them  the  starting-point  than 
the  foundation,  or  even  a  ladder  which  has  to  be  kicked 
away  (p.  164).  In  stating  them,  all  that  Formal  Logic 
does  is  to  put  into  words  the  pre-suppositions  with 
which  every  human  being  begins  his  life-long  investi- 
gation of  the  facts  of  the  universe.  In  a  vague  way 
we  learn  the  axioms  of  Logic  almost  before  we  learn  to 
speak,  and  a  few  years  later  we  are  freely  engaged 
in  applying  them,  with  small  reflection  upon  the 
possibility  of  their  being  misapplied.  The  rest  of 
our  life  is  spent  in  finding  out,  by  slow  and  discon- 
certing experience,  the  snares  of  their  application. 
What  we  want,  therefore,  from  a  science  of  Logic  is 
not  a  reminder  that  the  axioms  are  (in  the  abstract) 
|)erfectly  true,  still  less  an  optimistic  assurance  that 
we  need  not  think  of  them  as  misleading ;  rather,  we 
want  a  careful  exposition  of  the  ways  in  which,  when 
applied,  they  actually  mislead  us, — of  the  occasions 
when  they  break  down.  We  all  know  that  A  is  A  ; 
what  we  do  not  know  at  first  is  that  all  errors  in 
reasoning,  where  the  reasoning  is  anything  more 
than  a  pretence,  may  be  reduced  to  the  one  error  of 
taking  some  so-called  A  as  really  deserving  the 
name  (pp.  106,  136,  148,  173,  and  §  49). 

But  our  objection  goes  also  beyond  the  mere 
complaint  that  enough  is  not  done  to  guard  against 
the  most  natural  misapplications  of  these  abstract 
truths.  We  hold  that  to  state  them  at  all  is  to  state 
them  ambiguously,  and  so  to  put  an  obstacle  in  the 
way  of  discovering  the  need  for  care  in  their  applica- 
tion. The  ambiguity  of  the  statement  that  A  is  A 
— which  may  mean  either  that  real  A  is  real  A,  or 


334 


USE  OF  WORDS  IN  REASONING      partiv 


that  so-called  A  is  real  A  (pp.  20-23,  I  GO)  — is 
hidden  from  the  view  of  Formal  Logic  partly  through 
its  confusion  between  assertion  and  sentence  and 
partly  through  its  inability  to  recognise  that  a 
statement  which  claims  to  be  perfectly  abstract 
thereby  declines  to  claim  any  assertive  force  what- 
ever (p.  32).  Thus  the  formal  logician  is  prevented, 
or  at  least  hindered,  from  seeing  that  the  only 
way  to  make  the  sentence  '  A  is  A '  (taken  as  a 
statement  about  A)  do  more  than  express  a  question- 
begging  truism — the  only  way  to  make  it  an  applicable 
statement — is  to  interpret  it  as  meaning  *  so-called  A 
is  really  A ' ;  i.e.  as  laying  down  the  general  rule  that 
there  is  no  appeal  from  names  to  the  facts  behind 
them.  As  a  statement  not  about  A  at  all,  but  about 
(say)  the  nature  of  judgment  in  general,  the  sentence 
can  of  course  be  given  any  meaning  we  please 
(p.  159  11.) ;  but  if  we  elect  (as  the  ordinary  textbook 
does)  to  make  it  a  statement  about  A,  then,  if  it  is 
to  be  applicable,  things  or  cases  which  are  taken  as 
A  are  the  only  things  or  cases  it  can  re  tor  to. 

This  line  of  criticism  applies  not  only  to  the 
Law  of  Identity,  but,  as  we  have  seen,  to  the 
other  formal  foundations  of  Logic  equally  (pp.  92, 
102,  and  §  35).  In  so  far  as  any  supposed 
axiom  (about  the  nature  of  things,  or  about 
the  causal  connection  between  tliem)  is  left  purely 
abstract  and  unassailable,  it  tells  us  no  more  than 
that  A  is  A,  while  the  moment  we  turn  it  into  an 
applicable  statement  it  becomes  at  best  an  improvable 
half-truth.  And  ambiguity  is  the  source  of  all  the 
harm  these  axioms  do.  So  far  as  their  ambiguity  is 
unrecognised,  its  practical  effect  is  to  lend  support, 
by  allowing  a  shift  between   the  abstract   and   the 


CH.  xn,  ^69  THE  CASE  AGAINST  FORMAL  LOGIC  335 

applicable  meaning,  to  the  extremely  shaky  assertion 
that  things  are  what  they  seem  to  be,  or  what  most 
people  take  them  for;  which  is  precisely  what  the 
baby  and  the  savage  believe  until  they  have  learnt 
better.  And  since  the  whole  of  philosophy,  or  of 
science,  or  of  any  kind  of  experience,  consists  in  a 
more    or    less    elaborate    war    against     this    crude 

assumption,  one  does  not  see  what  can  be  gained 

except  the  preservation  of  error — by  holding  it  up 
for  reverence. 


§  69. — Appeal  for  a  Defence 

The  foregoing  account  of  the  shortcomings  of 
Formal  Logic  is  put  forward  in  the  hope  of  meeting 
with  corrections.  At  present  the  chief  difficulty 
which  the  opponents  of  Formal  Logic,  if  they  want  to 
l)e  fair,  have  to  contend  with,  is  that  so  little  express 
defence  of  it  is  to  be  found  in  the  books.  In  some  of 
the  older  ones,  such  as  Whately's,  it  is  defended 
against  objections  which  are  quite  different  from  those 
here  brought  forward,  and  most  of  which  it  is  difficult 
to  imagine  any  one  nowadays  seriously  making ;  but 
in  modern  textbooks  of  Formal  Logic,  it  is  either 
assumed  that  the  system  needs  no  defence,  or  else  the 
merits  of  *  Logic '  are  explained  almost  without 
reference  to  the  question  whether  it  is  the  more 
formal  or  the  less  formal  Logic  which  most  possesses 
them.  Let  me  quote  Mr.  Carveth  Read's  account 
of  them,'  as  an  illustration.  The  first  clause  runs  as 
follows: — 

>  Logic,   Deductive  and  Inductive,  p.    5.     Though  some  of  the   passages 
quoted  are  expressed  humorously,  I  take  them  as  intended,  on  the  whole 
to  make  a  serious  defence  of  the  traditional  Logic.     And  at  any  rate  they 
form  the  completest  attempt  at  a  defence  I  have  met  with. 


336 


USE  OF  WORDS  IN  REASONING       part  iv 


Logic  states,  and  partly  explains  and  applies,  certain  abstract 
principles  which  all  other  sciences  take  for  granted  ;  namely,  the 
axioms  above  mentioned. 

To  this  we  should  answer  that  the  value  of  the 
statement  of  the  axioms  depends  entirely  upon  the 
explanation  and  application  given  along  with  it  ;  that 
the  usual  explanation  of  the  logical  axioms  is  so  un- 
critical that  it  omits  altogether  to  point  out  their 
chief  defect  (ambiguity)  and  the  manner  in  which  it 
obstructs  progress;  and  that  the  only  application 
(riven  to  them  in  Formal  Logic,  is  to  cases  where 
there  is  no  dispute.  However  true  it  may  be  (as  Mr. 
Read  explains,  ibid.  p.  61),  that  Socrates  at  one 
moment  is  practically  the  same  person  as  Socrates 
five  minutes  later,  why  should  we  systematically 
keep  out  of  sight  the  extremely  numerous  cases  where 
a  given  thing  is  A  at  one  moment,  and  less  properly 
A  at  the  next  ?  And  change  in  time  is  only  one  of 
many  intluences  which  are  always  interfering  with 
the  axiom  that  A  is  A.  It  can  hardly  be  called  an 
uncommon  or  an  unimportant  experience  to  find  a 
difference  of  opinion  as  to  whether  *  A '  is  really  A 
or  not  (pp.  21-J--214). 

Mr.  Head's  second  clause  runs  as  follows  : — 

By  exercising  the  student  in  the  apprehension  of  these  truths, 
and  in  the  application  of  them  to  particular  propositions,  it 
educates  the  power  of  abstract  thought.  For  this  leason  Logic 
is  the  best  propaedeutic  to  Philosophy,  that  is,  to  Metaphysics 
and  Speculative  Ethics. 

Our  contention  here  is  that  the  defective  explana- 
tion and  application  just  spoken  of  can  only  be  said 
to  educate  the  power  of  abstract  thought  in  the  sense 
that  they  educate  the  power  of  shifting  between  two 
meanincts.     Such  a  power,  though  (as  we  noticed  in 


CH.  xn,  §  69  THE  CASE  AGAINST  FORMAL  LOGIC  337 

4i  49)  it  has  some  scientific  and  philosophical  value, 
needs  control  or  repression  rather  than  encouragement. 
Taken  Ijy  itself,  and  without  due  regard  to  its  dangers, 
we  cannot  think  it  a  good  propjedeutic  to  Philosophy, 
— except  so  far  as  the  doubtful  excuse  holds  good  that 
wild  oats  ought  to  be  sown  early.  At  any  rate  there 
seems  to  be  no  sufficient  reason  why  educational 
theories  should  ignore  the  fact  that  unmitigated 
abstractness  is  a  defect  in  thought,  and  that  thought 
as  it  grows  clearer  and  stronger  has  more  and  more 
grip  of  the  concrete. 

Thirdly,  Mr.  Read  says  : — 

Every  science,  when  well  expounded,  is  a  model  of  method, 
and  a  discipline  in  close  and  consecutive  thinking.  This  merit 
Logic  ought  to  possess  in  a  high  degree. 

It  certainly  ought,  we  admit.  But  the  question 
whether  Formal  Logic  does  possess  the  merit  of  being 
a  model  of  method  is  one  of  our  points  at  issue.  And 
in  regard  to  mental  discipline,  why  are  we  to  assume 
that  formality  in  our  Logic  makes  the  discipline  any 
better  ? 

Next  comes  a  longer  clause  : — 

As  the  science  of  proof,  Logic  gives  an  account  of  the  general 
nature  of  evidence,  deductive  and  inductive,  as  applied  in  the 
physical  and  social  sciences  and  in  the  affairs  of  life.  Observe  : 
the  general  nature  of  such  evidence.  It  would  be  absurd  of  the 
logician  to  pretend  to  instruct  the  Chemist,  Economist,  and 
merchant,  as  to  the  special  character  of  the  evidence  requisite  in 
their  several  spheres  of  judgment.  Still,  by  investigating  the 
general  conditions  of  proof,  he  sets  every  man  upon  his  guard 
against  insufficient  evidence. 

Of  course  Logic  does  not,  in  the  first  place,  teach  us  to  reason. 
We  learn  to  reason,  as  we  learn  to  walk  and  talk,  by  the  natural 
growth  of  our  powers,  with  some  assistance  from  friends  and 
neighbours.     But,  to  be  frank,  few  of  us  walk,  talk,  or  reason, 

22 


/ 


338 


USE  OF  WORDS  IX  IlEASOXiy^l       part  iv 


remarkfilily  well  ;  and,  as  to  reasoning',  Lo^ic  certainly  (juickens 
our  sense  of  )>a(l  reasoning,  both  in  others  and  in  ourselves.  It 
helps  us  to  avoid  heinir  misled  by  others,  and  tc)  correct  our  own 
mistakes.  A  man  who  reasons  deliberately,  manages  it  better 
after  studvinir  Loi'io  than  he  could  before, — if  he  tries  to.  if  he 
has  not  a  perverse  liking  fur  sophistry,  and  if  he  has  the  sense  to 
know  when  formalities  are  out  of  place.  There  are  some  mental 
qualities  that  a  man  can  oidy  get  from  his  father  and  mother. 

Our  objection  here  is,  tirst,  that  the  account  given 
by  Formal  Logic   of  the    nature  of  evidence   is   so 
general,  that  it  covers  good  and  bad  evidence  indi.^- 
criminately  (^  18) ;  that  absurd  as  it  would  doubtless 
be  for  the  mere  logician  to  pretend  to  be,  qvi'i  logician, 
a  specialist  in  Chemistry,  or  in  anything  else  except 
Logic,  yet  he  can  only  set  otlier  peoj^le  upon  their 
guard  ajrainst  iiisufticient  evidence   in  so  far  as  he 
trives   them   a   little   more   than    the  bare   outline  of 
sufficiency.      It  has  here  been  throughout  suggested 
that  the  best  he  can  do  is,  to  pay  special  attention  to 
sources  of  fallacy  in  so  far  as  they  are  effective  on  a 
wide  scale  ;  and  that  tlie  chief  of  these  is  ambiguity, — 
the  one  which  Formal  Logic  most  neglects  to  consider. 
Logic    so  transformed   might  really  quicken  our 
sense  of  bad  reasoning  ;  but  what  Formal  Logic  does 
is  only  to  quicken   it   in  the  least   interesting  and 
important  direction,  and  so  to  draw   our  attention 
away  from  the  serious  dangers.     In   fact,  we  agree 
with  Sir.  Read,  that  a  man  may  improve  his  reason- 
ing   habits    by    studying    Logic,    but  we  would  lay 
rather  more  stress  on  the  condition,  **  if  he  has  the 
sense  to  know   when   formalities  are  out  of  place." 
Why  should   our  possession  of  that  most  desirable 
sense  be  left  entirely  to  the  accidents  of  our  birth  ? 
And  specially,  why  should  our  education  do  all  it  can 
to  counteract  it  ? 


CH.  xn.  §  69  THE  CASE  AGAINST  FORMAL  LOGIC  339 
The  next  clause  is  also  a  lon^r  one  : — 

o 

One  application  of  the  science  of  proof  deserves  special 
mention  :  I  mean,  to  that  dei>artnient  of  Rhetoric  that  has  been 
the  most  developed,  relating  to  persuasion  by  means  of  oratory, 
leader-writing,  or  pamphleteering.  It  is  usually  said  that  Logic 
is  useful  to  convince  the  judgment,  not  to  persuade  the  will  : 
but  one  way  of  persuading  the  will  is  to  convince  the  judgment 
that  a  certain  course  is  advantageous ;  and  although  this  is  not 
always  the  readiest  way,  it  is  the  most  honourable,  and  leads  to 
the  most  enduring  results.  Logic,  in  fact,  is  the  backbone  of 
Rhetoric. 

Now,  it  is  in  view  of  these  last  four  uses  of  Lo^ic  that  it 
may  be  treated  as  an  Art.  As  a  science,  it  explains  the  relation 
of  truths  to  one  another,  especially  to  certain  first  principles  :  as 
an  Art,  it  regards  Truth  as  an  end  desired,  and  points  out  some 
of  the  means  of  attaining  it ;  namely,  to  proceed  by  a  regular 
method,  to  test  any  proposition  by  the  principles  of  Logic,  and 
to  distrust  whatever  cannot  be  made  consistent  with  them.  It 
does  not  give  anyone  originality  and  fertility  of  invention  ;  but 
it  enables  us  to  check  our  inferences,  revise  our  conclusions,  and 
chasten  the  vagaries  of  ambitious  speculation.  On  account  of 
this  corrective  function,  Logic  is  sometimes  called  a  Regulative 
Science. 


The  first  of  these  paragraphs  leaves  little  room  for 
improvement  except  in  one  particular.  Granting  it 
true,  in  a  sense,  that  Logic  is  the  backbone  of  Rhetoric, 
we  must  not  therefore  assume  that  Formal  Lode  is 
the  backbone  oigood  Rhetoric.  We  should  remember 
that  the  quality  of  any  Rhetoric  largely  depends  on 
that  of  its  backbone.  The  specimen  of  Rhetoric 
given  above,  at  p.  76,  admits  of  being  called  '  logical ' ; 
and  the  same  is  true  of  many  of  the  most  clap -trap 
arguments  on  political,  social,  and  economical  matters. 
The  question  whether  Formal  Logic  is  the  backbone 
of  good  Rhetoric  is  itself  part  of  our  question  at 
issue. 


340  USE  OF  WORDS  IN  REASONING      part  iv 

And  the  same  kind  of  criticism  applies   to   the 
second  paragraph  also,— that  the  explanations  given 
by  Logic,  whether  they  are  intended  to  have  a  practical 
aim  or  not,  are  more  or  less  satisfactory  or  useful  in 
proportion  to  the  character  of  the  Logic  which  pro- 
vides them.      Merely  because   it  is  the  aim  of  all 
Logic  to  make  its  explanations  as  good  as  possible, 
we  must  not  assume  that  Formal  Logic  is  the  kind 
of  Lof^ic  which  comes  nearest  to  this  ideal ;  and  we 
are  especially  bound  not  to  assume  it  when  that  is 
the  point  at  issue.       But  further  we  should  note- 
since  it  is  a  characteristic  defect  of  Formal  Logic — the 
unsatisfactory  conception  of  '  science  '  here  employed. 
In  whatever  sense  it  may  be  true  that  the  highest 
scientific  curiosity  soars  above  mere  practical  con- 
siderations, there  are  few  current  phrases  which  can 
more  easily  be  used  to  encourage  the  stagnation  of 
thought  (p.   47  n,).     The  clash   and  interaction  be- 
tween general  rules  and  their  particular  applications 
is  the  vital  element  in  science  (§5^  27,  50) ;  so  that  the 
attempt  to  explain  the  relation  of  any  supposed  truth 
to  first  principles  only  ceases  to  be  a  wordy  illusion 
when  this  artificial  barrier  between  the  aim  of  a  science 
and  the  aim  of  an  art  is  broken  down.     There  would 
be  no  check  upon   random  assertion  in  the  name  of 
science,  if  science  were  really  divorced  from  every  kind 
of  practical  consideration. 

One  more  plea  remains  : — 

"  Finally,  Logic  is  jit  lo.ist  a  refined  mental  exercise.  And  it 
needs  no  telescopes,  microscopes,  retorts  or  scalpels  ;  no  obser- 
vatories,  laboratories,  or  museums:  it  is,  therefore,  cheap  and 
convenient.  Moreover,  it  is  of  old  and  honourable  descent ;  a 
man  studies  Logic  in  very  good  company.  It  is  the  warp  upon 
which  nearly  the  whole  web  of  ancient,  mediaeval  and  modern 


CH.  XII,  §69  THE  CASE  AGAINST  FORMAL  LOGIC  341 

philosophy  has  been  woven ;  and  is  therefore  manifestly  indis- 
pensable to  a  liberal  education." 

The  mental  exercise  which  Formal  Logic  provides 
has  been  already  referred  to  (p.  312),  and  one  object 
of  this  book  has  been  to  show  certain  respects  in 
which  it  is  capable  of  much  greater  refinement.  The 
other  advantages  mentioned  belong  to  both  types 
of  Logic  equally,  except  that  our  chance  of  keeping 
level  with  our  own  times,  and  so  making  our  educa- 
tion sufficiently  liberal,  depends  on  our  power  of 
understanding  not  only  the  virtues  but  also  the  vices 
of  those  older  views  from  which  the  modern  ones  in 
all  their  variety  are  descended. 

On  the  whole,  then,  it  appears  that  there  is  little 
in  Mr.  Read's  defence  of  Formal  Logic  which  does 
not  apply  with  greater  force  to  Logic  in  so  far  as 
it  strives  to  avoid  formality.  The  virtues  claimed 
which  refer  to  Formal  Logic  exclusively  are  (1)  the 
statement  of  the  axioms,  as  distinguished  from  their 
explanation  ;  (2)  their  illustration  by  examples  of  an 
undisputed  kind  ;  and  (3)  the  education  in  *  abstract 
thought'  so  given.  In  themselves  these  do  not 
seem  to  be  a  sufficient  justification  for  restricting 
the  field  of  logical  operation  to  the  utmost  and 
obstructing  the  further  growth  of  logical  theory 
(pp.  35,  162,  219  ;  and  §§  27,  50). 

Still,  the  question  remains  open,  what  other  claims 
can  be  made  in  favour  of  Formal  Logic.  Let  us 
hope  that  some  believer  in  its  virtues  will  come 
forward  and  meet  as  directly  as  possible  those  parts 
of  our  whole  case  against  the  traditional  teaching 
system  which  seem  to  him  mistaken.  The  value  of 
such  an  attempt  will  depend,  of  course,  upon  its 
relevance  to  the  actual  objections  made ;  there  would 


342 


USE  OF   WORDS  IN  EEASONIXG       I'aut  iv 


be  no  point,  for  instance,  in  a  laboured  proof  of  the 
admitted  fact  that  Formal  Logic  has  some  value,  or 
that  every  Logic  must  be  to  some  extent  formal. 
The  question  is  whether  the  traditional  system  needs 
improvement,  and  what  are  the  lines  along  which  the 
improvement  should  proceed. 


CHAPTER    XIII 


HOW    LOGIC    MIOHT    BE    TAUGHT 

§  70. — A  Method  of  Simplification 

It  remains  now  to  (consider  l)riefly  the  question 
what  van  be  substituted  for  the  unsatisftictory  plan 
of  making  Logic,  for  teaching  purposes,  as  formal 
as  possible.  Granted  that  in  teaching  any  subject 
it  is  best  to  begin  with  relatively  easy  questions  and 
to  proceed  gradually,  what  other  way  of  doing  so 
can  be  suggested  than  that  of  restricting  the  inquiry 
by  means  of  postulates  and  assumptions  intended  to 
simplify  the  main  problem  by  postponing  portions 
of  it  for  future  investigation?  And  the  main 
problem  of  Logic  being  to  organise  our  knowledge 
of  the  difference  between  good  and  bad  reasoning, 
it  seems  at  first  difficult  to  conceive  any  other  way 
of  simplifying  it  than  by  separating  the  form  from 
the  matter  of  reasoning ;  taking  first  the  general 
aspect  and  then  the  particular  complications, — first 
the  outline  and  then  the  details  which  require  a 
closer  scrutiny.  Whatever  defects  this  plan  may 
have,  still  if  it  is  our  only  resource  we  must  put  up 
with  them,  or  else  cease  from  attempting  to  make 
the  subject  teachable. 

But  I  would  submit,  in  the  first  place,  that  the 


344 


USE  OF  WOIWS  IN  llEASONING      part  iv 


formal  rules  and  the  formal  definitions  are  not  the 
only  elementary  logical  matter  that  may  be  taught ; 
and  in  the  second  place  that  details  or  small  general- 
isations are  better  for  the  purpose  than  the  widest 
pi;inciples, — the  latter  being  rather  for  the  teacher 
to  consider,  and  for  the  student  to  investigate  only 
at  a  later  stage   of   his   work.      Our  chief  grounds 
for  thinking  the  old  plan   unsatisfactory  have  been 
summarised  in  the  preceding  chapter,  Init  they  need 
not  be  taken  as  merely  destructive.     They  involve, 
rather,  a  number  of   leading  principles  which  may 
be  used  in  directing  a  course  of  study,   while  the 
difficult  questions  as  to  the  truth  of  these  principles 
and  as  to  the  full  extent  of  their  consetiuences  may 
be  kept  in  reserve  as  long  as  the  teacher  pleases.     Of 
course  the  earlier  the  student  can  recognise  the  truth 
that  is  in  them,  the  better  ;  but  the  forcing  of  this  kind 
of  knowledge  is  a  doubtful  benefit.    The  result  usuallv 
seems  to  be  not  an  encouragement  of  philosophical 
thought,  but  rather  of  arrogant  partisanship  and  the 
use  of  catchwords  ill-understood. 

For  example,  we  cannot  expect  the  beginner  to 
see  at  once  all  the  harm  of  mechanical  rules  for 
distinguishing  bad  arguments  from  good  ones.  But 
what  we  can  do  is  to  avoid  encouraging  his  natural 
tendency  to  seek  for  short  cuts  of  this  kind.  He 
may  be  set  to  work  more  modestly  than  with  the 
hope  of  expressly  defining  once  for  all  the  difference 
between  good  and  bad  reasoning,  or  of  learning  off- 
hand how  to  discover  and  name  the  foults  of  any 
given  argument  he  meets  with  (p.  54).  And  the  same 
with  his  study  of  the  technicahties  ;  there  is  no  need 
to  trouble  him  at  first  with  the  reasons  why  he  is  not 
required  to  learn  concise  definitions  which  profess  to 


CH.  XIII,  §  70     HO  W  LOGIC  MIGHT  BE  TA  UGHT     345 

be  complete  and  final  (JJ  7),  but  his  attention  may  be 
directed  rather  to  the  doctrines  which  the  techni- 
calities are  needed  to  express,  and  through  them  to 
the  difficulties  of  interpretation  which  they  have  to 
contend  with. 

And  of  all  logical  doctrines  those  w^hich  relate 
directly  to  the  use  of  words  in  describing  facts,  and 
to  the  part  played  by  description  in  reasoning,  are 
the  most  elementary.  They  apply  to  the  commonest 
kinds  of  thought  and  yet  do  not  lose  their  value 
however  far  we  pursue  any  question  in  science  or 
philosophy.  Here  again  there  is  no  need  to  trouble 
the  beginner  w^ith  the  reasons  for  dwelling  upon  this 
subject, — reasons  which  have  been  given  at  some 
length  in  Parts  I.  and  II.  But  the  rudiments  of  it 
may  be  studied  before  he  sees  exactly  where  they 
are  going  to  lead  him  ;  in  the  meantime  this  study 
affords  room  for  much  criticism  of  loose  popular 
views,  and  thus  for  making  steady  and  gradual 
progress  in  logical  knowledge. 

Additional  help  might  be  given  by  using  some  of 
the  assumptions  of  Formal  Logic,  though  in  a  more 
guarded  manner.  The  neglect  of  context,  for  instance, 
may  be  made  a  really  useful  simplification  if  the  student 
is  sufficiently  warned  of  its  dangers  (pp.  242-244) ;  and 
the  same  with  the  confusion  between  assertion  and 
sentence.^  For  in  both  these  assumptions  the  harm 
arises  chiefly  through  taking  loose  definition  by 
type  for  exact  definition  by  characters.  And  even 
the  loosest  definition  will  often  serve  to  prepare  the 

'  Among  the  ordinary  effects  of  this  confusion  we  may  note  : — neglect  of 
ditnculties  of  interpretation  (pp.  19,  163,  260,  273,  and  §  58)  ;  tendency  to 
overlook  the  emptiness  of  abstract  statements  (pp.  33,  36)  ;  the  assumption 
that  it  is  easy  to  distinguish  between  '  one '  projiosition  and  *  more  than  one  ' 
(pj).  117,  143,  273,  301);  and  needless  comi)lication  of  logical  doctrines 
(§  66). 


346 


USE  OF  WORDS  IN  REASONING      part  iv 


ground  if  we  are  careful  not  to  take  it  at  more  than 
its  proper  value  (§  8). 

For  example,  the  identification  of  the  general 
name  with  the  descriptive  name  need  not  be  mis- 
leading if  it  is  openly  admitted  to  be  only  rough  and 
provisional  (p.  250).  A  doctrine  that  would  form  a 
useful  starting-point  is  that  all  descriptive  names,  as 
such,  are  indefinite  (^  39) ;  but  we  should  cause  un- 
necessary difficulty  if  at  first  we  raised  the  question 
what,  precisely,  is  a  descriptive  name.  Later,  the 
student  will  discover  that  a  descriptive  name  is  nothing 
else  than  the  middle  term  of  a  syllogism  (p.  35G) ;  but 
at  first  this  would  not  easily  be  made  clear  to  him. 
Therefore  it  seems  permissible  to  begin  by  roughly 
identifying  the  descriptive  name  with  the  kind  of 
name  which  grammar  recognises  as  a  general  name, 
class-name,  or  common  noun,  merely  explaining  that 
this  account  of  it,  though  mainly  correct,  contains  a 
certain  amount  of  error  which  may  for  the  moment 
be  neglected.  The  class -name  is  the  type  of  the 
descriptive  name,  though  it  is  not  true  that  all  class- 
names,  or  only  class-names,  are  descriptive. 

Starting  in  this  manner,  the  logical  instruction 
which  usefully  comes  before  the  direct  study  of  the 
leading  principles  may  be  divided  naturally  into 
three  parts:  'the  class -name  as  Predicate';  'Pre- 
dication and  Reasoning ' ;  '  Theory  and  Fact.' 

§  71. — Thk  Class-Name  as  Predicate 

The  peculiarities  of  the  class -name  are  easily 
shown,  whether  it  be  viewed  independently  of  con- 
text or  as  the  predicate  term  in  a  piece  of  description. 
In  the  first  of  these  aspects  it  is  evident  that  any 


CH.  xni,  §  7 1      HO  W  LOGIC  MIGHT  BE  TA  UGHT     347 

class-name,  as  such,  belongs  indifferently  to  a  number 
of  different  individual  cases.  And  in  the  second 
aspect  we  see  a  defect  that  arises  out  of  this  quality. 
Just  because  of  its  breadth  of  application — just 
because  it  purposely  neglects  the  difference  between 
the  members  of  the  class,  however  few  they  may  be 
— the  description  it  gives  of  any  one  member  is 
incomplete.  Each  member  possesses,  besides  the 
characteristics  which  give  him  a  place  in  the  class, 
certain  individual  peculiarities  which  it  is  the  very 
function  of  the  class-name  to  leave  out  of  account. 
The  class-name  thus  always  leaves  something  unsaid 
about  the  individual  member  (p.  165).  And  though 
subdivision  of  the  class  alleviates  the  defect  in  any 
given  case,  it  evidently  cannot  cure  it  (p.  175).  Sub- 
divide a  class  as  far  as  you  please,  and  there  always 
remains  room  for  further  subdivision  if  the  need  arises. 
It  is  this  possibility  of  future  need  for  subdivision  that 
constitutes  the  indefiniteness  of  class-names  regarded 
as  descriptive  (pp.  19G,  197).  The  class  X  necessarily 
l)lurs  the  distinction  l)etween  the  X  that  is  A  and  the 
X  that  is  not  A,  and  therefore  the  broad  description 
X  ftxils  to  say  which  of  these  alternatives  is  intended. 
This  may  be  called  the  fundamental  defect  of  the  class- 
name  when  used  as  a  predicate.  And  its  recognition 
leads  directly  on  to  the  other  truths  al)out  predication 
which  the  student  of  Logic  must  learn  to  substitute 
for  the  looser  views  of  common  sense. 

Criticism  of  loose  views  always  consists  in  finding 
unexpected  exceptions  to  general  rules,  but  this  often 
takes  the  less  direct  form  of  finding  fault  with  a 
distinction.^  In  order  to  criticise  the  rule  that  all 
A  are  B,  for  example,  it  is  not  always  necessary  to 

1  Several  examples  are  referred  to  in  §  73. 


'« 


348 


USE  OF  WORDS  IN  REASONING      part  iv 


i 


find  cases  of  A  which  are  not  B.  The  rule  is 
defective  not  only  when  it  can  be  shown  to  be  false, 
but  also  when  doubts  arise  about  its  precise  applica- 
tion,— when  a  difficulty  is  felt  in  deciding  which 
cases  are  properly  A  and  which  are  not  (§§  4-6).  A 
rule  in  this  vaorue  condition  is  even  more  effectivelv 
misleading  than  one  that  is  grossly  false  ;  the  ex- 
ceptions to  it  are  less  easily  seen,  since  it  can  onlv 
be  applied  and  tested  in  a  rough  way ;  and,  in 
consequence  of  this,  it  runs  a  special  risk  of  restini: 
upon  the  illegitimate  support  of  the  circular  argu- 
ment that  all  A  are  B  because  anv  case  which  is 
not  B  would  not  be  a  case  of  A  *  properly  so  called,' 
or  because  the  *  essence  '  of  A  is  to  be  B  ;  or,  in  other 
words,  that  A  is  B  because  it  really  is  so.^  Naturally, 
in  so  far  as  any  rule  draws  its  support  from  this 
kind  of  reasoning,  there  is  an  end  to  any  hope  of  im- 
proving it  (S  68).  Hence  the  attempt  to  improve 
logical  generalisations  has  to  be  ever  on  guard  against 
satisfaction  with  rules  that  are  nearly  true  and  there- 
fore useful  for  rough  purposes,  but  which  suffer  from 
this  taint  of  '  abstract ness '  or  vagueness  of  statement. 
That  is  why  so  much  of  the  work  of  the  logician 
consists  in  finding  fault  with  loose  distinctions. 

Now  if  all  class -names  are  indefinite  it  follows 
at  once  that  the  distinction  between  definite  and 
indefinite  ones  (or  as  the  older  Logic  used  to  call  it, 
univocal  and  equivocal)  is  loose  and  unsatisfactory 
(pp.  182,  207).  It  can  at  most  attempt  to  mark  off 
broadly  the  less  from  the  more  indefinite  ;  it  cannot  be 

'  As  examples  of  this  dancjer  we  may  note  :— The  '  Substitution  of 
Similars '  (p.  22)  ;  statements  of  *  tendency  '  (p.  32)  ;  certain  other  state- 
ments  (p.  38)  ;  circular  definitions  (p.  49)  ;  inductive  axioms  (pp.  95,  97, 
102)  ;  definition  of  '  reasoning; '  (p.  114)  ;  Liivv  of  Identity  (p.  160)  ;  Agassiz 
and  immutable  species  (p.  102  n.)\  degrees  of  indetiniteness  (pi..  180,  199, 
207). 


CH.  XIII,  !^  7 1      HO  W  LOGIC  MIGHT  BE  TA  UGHT     349 

trusted  to  tell  us  that  such-and-such  a  name,  since  it 
is  *  definite '  is  safe  from  any  further  inquiry  into  its 
meaning.  Moreover,  even  the  comparatively  modest 
distinction  between  the  less  and  the  more  indefinite 
has  the  defect  of  being  inapplicable  to  given  class- 
names  until  after  the  purpose  for  which  alone  we  can 
want  to  apply  it  is  satisfied.  The  only  conceivable 
purpose  of  the  distinction  is  to  mark  oft'  those  names 
which  need  definition  from  those  which  do  not,  but 
the  notion  of  degrees  of  indefiniteness  cannot  be 
given  any  meaning  which  bears  upon  this  question 
unless  the  '  more  indefinite '  names  are  completely 
identified  with  those  that  are  in  greater  need  of 
definition  (pp.  180,  199) ;  and  then  the  doctrine  that 
the  less  indefinite  any  name  is,  the  more  it  escapes 
this  need,  would  tell  us  only  that  a  name  escapes  the 
need  of  definition  just  so  far  as  it  really  does  so. 

The  distinction  between  univocal  and  equivocal 
(or  even  between  more  or  less  definite)  class-names 
is  thus  seen  to  form  an  insecure  basis  for  any  logical 
doctrine  restricting  the  need,  or  the  right,  of  enquiring 
after  a  definition  in  given  cases  ;  and  the  recognition 
of  this  negative  truth  leads  us  into  conflict  with 
several  other  loose  views  and  rough  definitions  which 
common  sense  is  inclined  to  take  as  trustworthy 
beyond  their  deserts.  Among  these  may  be  mentioned 
first  the  distinction  between  natural  and  artificial 
classes  (pp.  155-157),  and  the  view  that  some  classes 
— natural  ones  especially — have  a  *  correct '  meaning 
which  can  be  given  by  a  definition  and  then  used 
to  prevent  casuistic  doubts  from  being  raised.  Even 
the  so-called  natural  classes,  it  must  now  be  admitted, 
resemble  the  most  artificial  classes  in  the  fact  that 
the   class  -  members   are   different   from   each   other, 


350 


USE  OF  WORDS  IX  REASOXING      part  iv 


though  the  differences  may  be  less  obvious,  and  are 
usually  less  important,   on   the   whole,   than   in   the 
case  of  classes  which  arc  plainly  artificial.    If  (as  with 
two  apparently  pure  specimens  of  gold)  the  differences 
are  obscure,  this  determines  only  the  likelihood,  not 
the    certainty,  that    difficult    questions  of  definition 
will  never  usefully  arise  when  the  name  is  used  as 
a  predicate  (^  :59,  and  pp.  11)0-194,  l>05  ff.);  and  an 
unlikely  question  when  it  does  arise  is  more  perplexing- 
than  a  likely  one.     Nor  does  the  gener.d  utility  of  a 
class-name  save  it  from  beini:?  of  doubtful  value  now  and 
then.     For  instance, the  notion  'Truth'  (the  class-name 
'true  statement')  is  of  the  utmost  utility,  and  yet  the 
more  convinced  we  are  that  we  can  clearly  separate 
truth  from  error  the  less  prepared  are  we  to  rec^ognise 
the  traces  of  error  that   certain   kinds   of  valuable 
half-truth    contain.       Strict   Logic   here  comes  into 
opposition    with    the    tenden(,*y  of   popular    thought 
to  stiHe    questions  which   suffer  from   this  kind    of 
paradox,   without   im^uiring  into   their  justification  ; 
a  tendency  which    finds   general    expression    in    the 
'  Law  of  Identity.'     Instead  of  accepting  the  axiom 
that  A  is  A,  in  the  only  sense  in  which  it  can  be 
supposed  to  give   infiirmation   about  the  use  of  the 
class-name  A,  the  logician  ought  to  supplement  this 
half-truth  of  common  sense  by   the   retlection   that 
though    the    world's    application    of    a    well-known 
class  -  name    is   generally   more    right   than   a  clever 
young  person  imagines,  yet  occasionally  the  reverse 
is    the    case ;    and    room    must    be    made    for    this 
possibility   in   any   careful   logical  doctrine.      Taken 
strictly,  and  interpreted  as  applicable  generalisations, 
the   Law^s  of  Thought  involve,  as  we  saw  (p.   1G4), 
the  assumption  that  ambiguity  is  impossible.     Since, 


CH.  xni,  ^71      HO  W  LOGIC  MIGHT  BE  TA  UGIIT     35 1 

how^ever,  this  would  be  too  absurd  a  position  for  even 
the  most  elementary  Logic  to  take  up,  and  since  it 
is  also  easier  not  to  interpret  them  quite  so  strictly, 
their  usual  effect  is  to  produce  a  milder  form  of  the 
same  assumption,— namely,  that  ambiguity  is  a  fault 
that  may  be  reckoned  as  of  small  account  (p.  177); 
or  as  so  exceptional,  and  so  seldom  a  serious  cause  of 
error,  that  it  bears  much  the  same  relation  to  thou^rht 
in  general  that  puns  bear  to  the  ordinary  use  of 
language  (pp.  184,  186). 

The  student  should  therefore  l)e  guarded  ao-ainst 
the  natural  impression  that  he  is  here  being  troubled 
to  notice  an  out-of-the-way  fact  which  can  scarcely 
ever  be  of  practical  service.  On  the  contrary,  the 
admission  of  this  apparently  far-fetched  truth  is  of 
interest  and  value,  not  only  for  its  occasional  direct 
application,  but  because  it  has  also  some  important 
consequences;  its  opponents  may  regard  it  as  the 
letting  out  of  the  w\aters,  while  its  supporters  will 
picture  it  rather  as  the  removal  of  a  blank  wall  that 
bars  the  light.  For  in  the  first  place  it  helps  to 
explain  the  process  by  which  our  knowledge  of 
Nature  growls,  and  to  further  that  process  in  various 
indirect  ways  (chap.  viii.).  And  in  the  second  place, 
as  a  means  to  this  end,  and  as  a  subject  of  more  im- 
mediate interest  at  the  beginning  of  a  course  of  logical 
study,  it  helps  us  in  getting  a  view  of  the  nature  of 
reasoning,  and  of  the  defects  to  which  reasoning  is 
liable,  especially  those  defects  which  are  all  the  more 
misleading  because  they  are  not  easily  seen. 


352 


USE  OF  WORDS  IN  REASONING      part  iv 


§  72. — Predication  and  Reasoning 

For,  first,  there  is  then  no  longer  any  difficulty  in 
admitting  that  every  predication,  with  a  class-name 
as  predicate,  is  liable  to  be  disputed  on  the  ground 
that  some  other  definition  of  the  predicate  term  is 
contemplated  than  that  whicli  suits  the  present 
purpose.  Of  course  a  good  many  predications  are 
liable  also  to  be  disputed  on  a  less  subtle  ground 
than  this, — namely,  on  the  ground  that  S  does  not 
really,  l)ut  only  apparently,  come  under  the  gene7*al 
definition  of  A.  But  disputes  of  this  nature  are 
more  easily  settled,  and  therefore  of  smaller  interest 
to  Logic,  than  where  S  admittedly  comes  under  the 
general  definition  of  A,  but  where  one  party  suspects, 
while  the  other  does  not,  that  the  case  is  exceptional, 
and  that  a  further  subdivision  of  the  class  A  is  here 
required  (§  47).  Since  progress  in  our  knowledge  of 
Nature  consists  mainly  in  improving  rules  by  register- 
ing exceptions,  any  habit — such  as  excessive  regard 
for  a  general  definition,  or  for  the  maxim  that  A  is 
A — which  hinders  our  view  of  exceptions,  is  one 
which  Logic  cannot  be  justified  in  encouraging.  One 
does  not  need  to  learn  how  to  miss  seeing  exceptions ; 
that  faculty  is  a  widespread  natural  gift,  like  other 
kinds  of  limited  perception. 

And  next,  when  we  ask  what  is  meant  by  the 
'  purpose  *  of  a  predication,  the  answer  is  that  tliat 
is  always  the  drawing  of  some  conclusion  syllo- 
gistically  (§§  27,  28,  and  p.  167);  and  that  there- 
fore the  meaning  of  a  predicate  term,  in  cases 
where  there  is  any  conHict  between  general  and 
particular   meaning,    is   determined   by    the   conclu- 


CH.  xni,  §  72      ffO  W  LOGIC  MIGHT  BE  TA  TIGHT     353 

sion  which  the  predication  is  meant  to  support. 
Naturally  it  is  only  where  the  confiict  between 
general  and  particular  meaning  arises,  or  in  other 
words  where  the  audience  have  a  suspicion  that 
some  false  inference  is  drawn,  based  upon  the  general 
resemblance  of  S  to  the  rest  of  the  class  A,  that 
any  reference  is  made  to  the  special  purpose.  But 
that  amounts  only  to  saying  that  such  reference  is 
not  made  where  the  assertion  is  either  plainly  false 
or  plainly  true ;  and  these  are,  from  a  logical  point 
of  view,  a  small  and  unimportant  class  of  assertions. 
The  more  careful  we  are  in  distinguishing  between 
truth  and  error,  the  more  our  attention  is  drawn  to 
the  prevalence  of  the  intermediate  class  of  state- 
ments, where  S  is  A  in  one  sense,  but  not  in  another, 
and  specially  where  S  is  A  in  a  broad  and  general 
sense,  but  where  this  fact  is  used  to  support  con- 
clusions it  will  not  properly  cover.  It  is  in  these 
cases  that  criticism  usefully  takes  the  line  of  re- 
membering that  we  cannot  intelligently  assent  to  a 
statement  until  we  are  clear  about  its  meaning,  and 
that  the  final  account  of  its  meaning  is  not  given  by 
the  general  definition  of  its  terms,  but  by  the  purpose 
of  tlie  moment. 

A  study  of  tlie  nature  of  predication,  and  of  the 
risk  it  always  runs  owing  to  the  indefiniteness  of 
class-names,  leads  in  this  manner  to  a  view  of  the 
syllogistic  process,  and  its  special  danger  the  am- 
biguity of  the  middle  term.  Every  predicative 
assertion,  it  now  appears,  is  in  one  aspect  a  minor 
premiss  (p.  276).  There  is  a  conclusion  to  which  it 
leads,  and  a  major  premiss  connecting  it  with  that 
conclusion.  The  question  being  asked  whether  S  is 
A,  a  suspicion  arises  that  the  answer  depends  on  the 

23 


354 


USE  OF  WORDS  IX  REASONIXG      i»akt  in- 


meaning  given  to  '  A,' — the  suspicion  that  though  S 
may  be  A  in  a  sense,  it  is  not  so  in  the  sense  that 
warrants  the  conclusion  intended  to  follow  from  it. 
And,  if  the  suspicion  is  justified,  then  we  have  a  case 
of  the  typical  deceptive  syllogism  ;  where,  though 
each  premiss  taken  by  itself  may  be  tiue,  yet 
when  they  are  put  together  the  conclusion  is  faulty 
through  ambiguity  of  the  middle  term  (pp.  l"^*?, 
134). 

From  this  aspect  of  the  syllogism,  where  the 
relation  between  premisses  and  conclusion  is  use«l 
in  raising  the  (question  whether  the  minor  premiss  is 
true,  it  is  an  easy  step  to  the  other  aspect  of  it 
where  the  truth  of  the  conclusion  is  the  matter  in 
dispute.  The  syllogistic  framework  and  its  re- 
quisites remain  exactly  the  same  whatever  use  it  is 
put  to.  We  may,  for  instance,  have  as  major  premiss 
a  mere  definition, — a  postulate  instead  of  a  generalisa- 
tion. And  then  the  possible  doubt  attaches  only  to 
the  minor  premiss  and  conclusion.  But  we  may  also 
easily  conceive  another  syllogism  in  which  the  asser- 
tion directly  questioned  is  the  conclusion,  and  where 
accordingly  both  premisses  are  on  their  trial.  In 
other  words,  any  statement  of  fact  may  have  its 
own  grounds  in(|uired  into,  besides  l)eing  used  to 
lead  on  to  further  conclusions.  Behind  any  state- 
ment of  fact  there  are  always  other  statements  of 
fact  and  the  theories  which  mve  the  latter  their 
relevance  (pp.  60,  82). 

There  is  very  little  that  need  be  taught  about  the 
Syllogism,  since  the  process  itself — which  is  merely 
that  of  bringing  a  particular  case  under  a  general  rule 
(pp.  62,  72-74,  2D4) — is  used  instinctively  by  every 
one  from  early  childhood  onwards ;  and  if  it  be  true 


CH.  xiii,  §  72      HO ]V  LOGIC  MIGHT  BE  TAUGHT     355 

that  there  are  any  lower  animals  whose  thoughts  are 
cast  in  a  different  mould,  we  have  no  beginnings  of  a 
conception  what  that  mould  (ian  be.^  AVhat  we  have 
not  got  by  instinct  is,  first,  the  conscious  analysis  of 
syllogistic  thought  into  the  two  premisses  and  the 
conclusion ;  and  secondly,  a  knowledge  of  the  ways 
in  w^hich  words  deceive  us  into  taking  a  faulty 
syllogism  as  correct.  The  analysis  is  only  useful  in 
so  far  as  it  is  made  to  help  forward  the  latter 
branch  of  knowledge.  It  is  partly,  no  doubt, 
because  the  dog  has  had  no  instruction  in  technical 
Logic  that  he  argues  so  contentedly  about  the  scald- 
ing qualities  of  cold  water.  The  middle  term  he 
uses  is  the  concept  corresponding  to  our  English 
word  '  water,'  and  he  neglects  to  subdivide  the  class 
into  hot  and  cold. 

Now^  the  ways  in  which  words  deceive  our  thoughts 
are  divisible  into  two  main  kinds,  of  which  only 
one  is  treated  by  Formal  Logic.  There  may  be  lax 
interpretation  of  sentence  forms,  and  there  may  be 
ambiguous  statement  either  of  the  particular  fact 
or  of  the  general  rule.  As  regards  the  former,  we  have 
seen  (g  (jQ)  that  any  rules  for  interpreting  sentences  are 
either  purely  grammatical  and  customary — and  then 
they  can  only  serve  as  a  very  rough  guide  to  the 
meaning  actually  intended — or  else  they  are  conven- 
tions independent  of  general  custom,  conventions 
made  by  formal  logicians  in  exactly  the  same  way  as 
the  symbolic  logician  postulates  the  meaning  of  his 
symbols ;  for  example,  the  rule  that  '  some '  shall 
mean  *  some  at  least '  and  not  '  some  only.'  The 
mistake  that  Formal  Logic  makes  is  in  giving  such 
rules  too  much  importance.     They  are  in  no  sense 

*  A  regards  inference  '  from  particulars  to  particulars  '  see  §  25,  and  p.  304. 


356 


USE  OF  WORDS  IN  REASONING      part  iv 


binding,  and  what  importance  they  have  consists  in 
pointing  out  certain  kinds  of  doubt  as  to  meaning 
that  frequently  occur  and  that  need  removing  by 
interrogation.  For  this  reason  it  may  be  worth 
while  to  call  the  student's  attention  to  some  of  the 
eases — such  as  the  doubt  whether  *  All  A  are  B '  is 
or  is  not  intended  to  assert  also  that  all  B  are  A,  or 
the  doubt  whether  '  Some  A  are  B '  is  meant  to  imply 
also  that  some  are  not  (pp.  300,  303).  No  harm 
can  be  done  by  this  kind  of  instruction  so  long  as 
we  avoid  supposing  that  certain  meanings  attached 
to  certain  forms  of  sentence  would  be  illogical.  Even 
when  the  expression  deserves  to  be  called  slovenly 
rather  than  epigrammatic,  still  there  is  a  difference 
between  slovenly  expression  and  slovenly  thought 
(pp.  77,  78).  Logic  has  enough  to  do  without  under- 
taking to  be  a  judge  of  literary  style. 

It  is  therefore  the  risk  of  ambiguous  middle  that 
Logic  has  chiefly  to  consider  in  its  view  of  the 
syllogistic  process,  and  a  study  of  the  nature  of  pre- 
dication (showing  the  necessary  indefiniteness  of  class- 
names  when  used  as  predicates)  prepares  the  way  for 
this.  Having  now  seen  that  every  predicative  state- 
ment gets  its  meaning  as  a  minor  premiss,  and  also 
that  every  statement  of  fact  gets  its  meaning  in  so 
far  as  the  fact  is  brought  under  general  rule  (and  thus 
forms  a  minor  premiss),  the  student  will  see  also  that 
every  statement  of  fact  is  descriptive  statement.  Thus 
he  may  now  enlarge  his  notion  of  the  descriptive 
name,  ceasing  to  identify  it  with  the  general  name, 
and  conceiving  it  as  the  middle  term  of  a  syllogism. 
Any  name,  it  now  appears  (whether  Grammar  would 
call  it  a  general  name  or  not)  is  descriptive  when 
used  as  a  middle  term,  and  in  no  other  usage.     It  is 


r 


\ 


CH.  XIII,  ^  72     HO  W  LOGIC  MIGHT  BE  TA  UGHT     357 

in  this  usage  only  that  a  name's  indefiniteness  can 
cause  ambiguity  (§  43,  and  p.  262). 

Hence,  too,  we  get  some  understanding  of  the 
peculiar  difliculties  that  are  always  encountered  in 
induction, — in  basing  general  rules  upon  particular 
cases  observed.  The  student  might  next  enter  upon 
that  most  important  branch  of  logical  inquiry,  the 
attempt  to  improve  our  rough  common-sense  views 
of  the  relation  between  theory  and  fact.  When  it  is 
sought  to  prove  syllogistically  that  S  is  P,  three 
things  are  required, — the /ac^  that  S  is  M,  the  theory 
that  M  indicates  P,  and  grounds  for  believing  that  M 
is  here  free  from  ambiguity, — or,  in  other  words,  that 
this  fact  and  theory  hold  good  not  only  as  indepen- 
dent statements  true  in  some  sense  or  other,  but  even 
when  they  are  put  together  as  premisses.  Here  we 
begin  to  see  the  defects  of  any  separation  Ijetween 
deductive  and  inductive  Logic ;  the  binding  force  of 
a  syllogism  cannot  be  understood  except  so  far  as  we 
understand  what  is  involved  in  avoiding  ambiguous 
middle,  and  to  do  this  we  have  also  to  understand 
how  general  theories  of  causal  connexion  (M  indicates 
P)  are  derived  from  facts  observed,  how  they  are 
strengthened  by  them  and  criticised  by  them,  and 
generally  how  fact  and  theory  envisage  each  other 
(pp.  66,  71,  84,  94).  The  question  whether  S  is  or  is 
not  the  kind  of  M  that  indicates  P,  is  of  vital  import- 
ance in  judging  the  validity  of  a  syllogism,  and  it 
can  only  be  studied  by  considering  questions  which 
are  commonly  reckoned  as  belonging  to  inductive 
Logic. 


I. 

1 


358 


USE  OF  WORDS  JN  IIEASUSJNG       I'ahtiv 


§  73. — Theory  and  Fact 

From  this  point  onward,  further  steps  may  be 
taken  more  rapitlly.  Theories  being  generaHsations 
which  pretend  to  cover  particular  cases,  and  facts 
being  of  wliolly  unspecified  content  except  so  far  as 
they  are  described  in  general  terms,  it  follows  that 
the  (juestion  whether  a  given  theory  is  true  depends 
in  tlie  first  place  upon  the  absence  of  facts  that  con- 
tradict it,  wliilo,  on  the  other  liand,  the  question 
whether  an  apparently  contradictory  fact  is  really  an 
exception  to  the  rule  depends  upon  the  c-orrectness  of 
that  fact's  description.  The  chief  thing  to  avoid  is 
any  cheap  solution  of  this  difficulty,  such  as  the 
device  of  making  the  assertion  of  theory  abstract  and 
undeniable.  Where  a  word  X  has  many  shades  of 
meaning  in  common  usage — say,  the  word  '  liberty,* 
or  the  word  'civilisation' — we  often  find  that  a 
general  assertion  about  X  becomes  less  open  to  attack 
by  contradictory  instances  when  we  explain  that  some 
of  the  looser  meanings  of  the  word  are  left  out  of 
account.  These,  we  may  say,  are  only  cases  of  X  by 
courtesy,  or  on  the  surface,  or  by  some  traditional 
misuse  of  the  term.  X,  when  it  really  deserves  to 
be  called  X,  is  Y.  And  only  a  narrow  line,  easily 
overstepped,  exists  between  this  legitimate  and 
often  almost  unavoidable  procedure,  and  that  of 
declining  to  allow  any  case  to  be  called  X  until  we 
know  that  it  is  Y.  This  is  one  of  the  great  dangers 
of  theorising, — that  in  our  search  for  essential  con- 
nections we  shall  refine  and  abstract  until  the  whole- 
some criticism  exercised  by  *  fact,'  or  concrete  cases, 
becomes    impossible    (§  G8).       AVhen    that    point    is 


I 


ci!  XIII,  i;  73      HO  W  LOGIC  MIGHT  BE  TA UGHT     359 

reached,  our  supposed   generalisation   has   dwindled 
away  to  a  mere  question-begging  truism. 

A  partial  recognition  of  the  complex  relation  thus 
existing  between  theory  and  fact  is,  no  doubt, 
common  enough.  Everyone  knows  that  theories 
ought  to  stand  the  test  of  fact,  and  that  since  facts 
are  not  always  what  they  seem,  an  apparent  excep- 
tion to  a  rule  may  turn  out  not  to  be  an  exception 
after  all.  But  a  much  fuller  recognition  of  the  way 
in  which  facts  and  theories  aid  and  criticise  each  other 
is  possible  when  we  have  understood  why  indefinite- 
ness  is  not  merely  an  occasional  incident  of  descrip- 
tive language,  but  is  a  fundamental  quality  of  it 
(p.  325).  For  then  we  find  a  rational  ground  for  our 
otherwise  vague  and  hesitating  criticism  of  certain 
loose  distinctions,  whose  evident  convenience  (within 
proper  limits)  is  constantly  inducing  us  to  overlook 
their  faults.  Chief  among  these  are  the  distinction 
between  certain  and  doubtful  facts  (p.  146),  and  be- 
tween undeniable  generalisations  and  questionable 
ones  (p.  88),  their  faults  being  precisely  analogous  to 
those  of  the  distinction  between  perfect  and  imperfect 
definiteness,  or  between  complete  and  incomplete 
description.  Since  anything  which  professes  to  be 
a  truth  has  to  be  stated  in  language,  it  is  always  a 
statement  of  fact  or  a  statement  of  theory  that  we 
have  to  deal  with,  not  fact  or  theory  considered  some- 
how apart  from  our  only  instrument  for  expressing 
them  (pp.  122,  142,  227,  228).  Hence  the  defects 
which  are  inherent  in  language  must  also  be  taken 
into  account  in  examining  a  statement  of  either  kind, 
and  the  result  is  an  increased  power  of  rationally 
criticising  facts  and  theories,  however  superficially 
plausible   they  may  be.      We   no  longer   trust  the 


4 
1,4 


f 


360 


USE  OF  WORDS  IN  REASOXrXQ       part  iv 


i 


i 


common  distinction  between  the  *  bare '  statement 
and  the  descriptive  statement  of  a  fact,  or  imagine 
that  any  fact  as  stated  is  free  from  theory  (§  31); 
we  no  longer  trust  the  distinction  between  abstract 
and  concrete  assertions  (pp.  255,  256,  270) ;  but  we 
recognise  that  any  statement,  if  purely  abstract,  would 
fail  to  be  an  assertion,  and  that  all  general  statements, 
in  so  far  as  they  are  assertive,  are  abstract  and  con- 
crete at  once,  their  quality  of  abstractness  being  the 
source  of  their  vagueness  and  consequent  misleadinor 
power, — the  very  thing  which  it  is  the  task  of  science 
to  diminish  as  persistently  as  possible.  Casuistry 
is  thus  seen  to  be  the  mainspring  of  the  progress  of 
knowledge. 

Two  other  distinctions,  commonly  trusted  beyond 
their  deserts,  are  also  discredited  by  this  line  of 
criticism, — the  distinction  l)etween  questions  of  fact 
and  questions  of  meaning  (§  49),  and  the  distinction 
between  a  *  single*  fact  and  a  group  of  facts  (j^i  18, 
and  pp.  94,  173).  As  regards  the  former  of  these, 
its  influence  is  directly  antagonistic  to  a  clear 
conception  of  the  work  that  is  everywhere  waiting 
to  be  done  by  casuistry.  However  great  may  be 
our  personal  admiration  for  Dr.  Johnson,  yet  it  is 
clear  that  if  all  the  questions  which  he  was  in- 
clined to  regard  as  simple  ijuestions  of  fact  had  re- 
mained to  this  day  in  so  flat  a  condition,  our  stock  of 
knowledge  would  have  been  considerably  poorer  than 
it  is.  Readiness  to  '  make  an  end  on't '  is  hardly  the 
way  to  prosecute  an  enquiry  with  vigour,  and  though 
practical  considerations  may  often  justify  such  readi- 
ness in  a  given  case,  there  is  all  the  difierence  between 
ceasing  an  inquiry  for  a  time  through  force  of  cir- 
cumstances and  imagining  that  such  closure  (;an  be 


CH.  xiii,  s  73      HO  W  LOGIC  MIGHT  BE  TA  UGHT     361 

permanent  or  should  be  encouraged  without  special 
reason.  The  mere  habit  of  preventing  questions  of 
fact  from  becoming  questions  of  meaning  is  not  in 
itself  of  scientific  value,  but  only  so  far  as  hurry  or 
other  necessity  drives  us  to  put  up  with  a  makeshift 
answer  till  better  opportunities  are  found. 

The  faults  of  the  distinction  between  single  facts 
(or  single  circumstances)  and  complex  ones  are  plainly 
of  direct  importance  to  our  view  of  the  difference 
between  good  and  bad  reasoning.  To  take  a  fact  as 
single  when  it  is  really  complex  is  the  same  thing  as 
to  submit  the  fact  to  insuflicient  analysis.  In  ji^^  12 
and  13  we  saw  how  in  syllogistic  reasoning  this  is 
the  source  of  aml)iguous  middle.  The  fact  S  is 
described  as  M,  and  if  we  forget  that  this,  being  a 
general  name,  is  indefinite,  we  jump  uncritically  to 
the  conclusion  which  follows  from  an  accepted  rule 
that  M  indicates  P.  To  take  precautions  against  the 
risk  of  faulty  connection  between  the  premisses  is  to 
look  beyond  the  fact's  general  nature  to  its  individual 
peculiarities.  However  simple  it  may  appear  when 
regarded  merely  as  a  member  of  the  class  M,  this 
aspect  of  it  is  never  all  that  the  fact  contains.  It  is 
made  up  of  details,  which  the  name  M  may  hide  l)ut 
cannot  abolish  (p.  69).  It  is  only  a  '  single '  fact, 
therefore,  so  long  as  we  are  content  to  regard  it  as 
single  (p.  173);  and  to  inquire  into  its  right  to  the 
name  M  with  a  view  to  the  indication  of  P  is  to 
break  it  up  into  a  group  of  facts,  of  greater  or  less 
importance  to  the  imagined  connection.  Thus  the 
utmost  verbal  simplicity  in  the  description  of  a  fact 
has  nothing  corresponding  to  it  in  the  concrete 
world,  and  to  forget  this  is  to  open  the  door  to  faulty 
reasoning. 


N 


i 


362 


USE  OF  WORDS  IN  REASONING       i'art  iv 


Similarly  when  the  problem  is  to  judge  the  precise 
causal  relation  between  two  facts  ol)serve(l.  What  we 
observe  is  the  happening  of  facts,  but  in  order  to  con- 
ceive them  as  such  and  such  facts  we  have  to  use 
general  names.  We  have,  therefore,  to  select  out  of 
all  that  is  really  going  on  before  us  certain  partial 
aspects  in  which  the  occurrences  may  be  viewed ;  we 
have  to  simplify  the  occurrences  artificially.  And  the 
difference  between  careless  and  careful  work  of  this 
kind  evidently  depends  upon  our  power  to  remember 
that  the  simplification  is  artificial  and  may  be  recon- 
sidered and  done  over  again  in  other  ways  (pp.  127, 
13G,  288,  28D).  Because  we  have  called  the  facts  X 
and  Y  (or  A  and  a)  we  have  not  thereby  closed  the 
question  whether  some  of  the  hitherto  unconsidered 
details  in  them — details  obscured  by  the  names  em- 
ployed— do  not  deserve  greater  consideration.  Fal- 
lacy, in  inductive  reasoning,  consists  in  overlooking 
details  which  are  wrongly  hidden  by  a  general  name. 

Along  these  lines  the  student  may  arrive  at  the 
view  that  mistakes  in  reasoning  are  nothing  but 
mistakes  in  the  facts  from  which  the  reasoning 
proceeds, — a  view  which  subjects  the  common  dis- 
tinction between  reasoning  and  judgment  to  the 
same  kind  of  criticism  as  the  other  distinctions  above 
noticed.  He  will  find  that  there  is  no  unreasoned 
judgment,  and  no  reasoning  process  apart  from  its 
subject-matter ;  but  that  in  every  judgment  more  or 
less  criticism  is  entangled  (p.  116),  such  criticism  being 
the  element  in  any  judgment  which  makes  it  a  reasoned 
judgment  as  contrasted  with  what  an  unreasoned 
judgment  would  be  if  such  a  thing  could  be  found. 
In  forming  any  judgment  we  use  facts  and  theories, 
or  new  knowledge  and  old,  both  these  aids  to  judgment 


CH.  xni,  §  73      HOW  LOGIC  MIGHT  BE  TAUGHT      363 

being  at  all  times  liable  to  revision  and  improvement. 
And  revision  always  takes  place  in  the  same  way, — 
through  finding  that  a  fact  described  as  A  might 
better  have  had  a  different  predicate.  The  case 
where  our  newly  observed  facts  are  wrongly  observed 
has  just  been  spoken  of;  and  the  case  where  our 
stored -up  general  knowledge  is  faulty  is  only  the 
same  thing  at  another  remove.  Where  we  have 
accepted  a  wrong  view  of  the  causal  connection 
between  X  and  Y,  which  leads  to  our  reading  a 
wrong  meaning  into  a  newly  observed  fact,  the  error 
did  not  originate  from  nothing,  but  is  traceable  to  a 
previous  misconception  of  ftict  observed.  Our  modern 
errors  therefore  have  a  pedigree,  and  Logic  will  re- 
main an  almost  useless  study  so  long  as  we  forget 
that  it  is  in  the  subject-matter  of  reasoning,  not  in 
any  abstract  '  reasoning  process,'  that  all  effective 
error  is  concealed. 


v 


INDEX 


'A     aud    'so-called    A/   111.112, 

160 
Abstract  as  'vague,'  31,  "254,  256 
Abstract  definitions,   49,    105,    110, 

161 
Abstract    names,    in    (Irannnar   and 
Fonnal     Logic,      253    11".  ;     as     a 
linguistic  device,  256  ;  their  con- 
notation, 257 
Abstract  statements,   nature    of,   30 
tr.,  160   tr.,   226,   270;    examples 
of,   21-23,   32,    92,    101-103;    in 
Cieometry,  33  If. ;  justification  for, 
31,  219  ti. 
Accident  and  essence,  in  events,  103- 
107,    124,    148  ;    in    class-names, 
152,  167  ;  in  i»roi>osition8,  269  ff. 
Atfiniiative    and    negative    i)ro}>08i- 

tions,  263  11. 
Agreement  and  Ditierence,  methods 

of,  90 
Ambiguity,  in  general,  48,  cha]*.  vii. ; 
tonfused  with  indefiniteness,  178 
tf. ;  occurs  only  in  assertions,  183, 
185-188,  199,  203;  entirely 
destroys  meaning,  188,  201  : 
extent  of  its  iK)ssibility,  176  tf.. 
228  ;  least  effective  when  obvious. 
180,  187,  190  ;  leads  to  sub- 
division of  a  class,  196-197,  234  : 
as  attaching  to  M,  66-71,  75.  82- 
84,  133-134  :  its  imjtortance,  136- 
137,  193,  219  tf.  ;  its  neglect  by 
Formal  Logic,  164,  182,  181,  199  ; 
its  discovery,  195  tf.,  218;  its 
removal,  202-204 
Analysis  as  employed  in  rea.soning, 

66,  69,  75,  96,  117 
Antecedent  and  consequent,  in  hypo- 
theticals,  273-274,  278-279,  297  ; 
in  causation,  102-106,  135 
Ay>i)lication  and  meaning,  10,  20  tf.; 
36,  92,  130 


Artifice,  need  for,  10;>,  1^*7 

Artificial  and  natural  classes,  152- 
157 

Assertion,  kinds  of,  259  11.  ;  con- 
fused with  sentence,  17-19,  345 
71.  ;  claims  to  be  true,  281,  284 

Assertoric  and  modal,  280 

Assumptions,  ojten  and  surreptitious, 
132;  of  Formal  Logic,  16,  17, 
and  cha}».  xii,  ;  for  methodical 
pur{»oses,  310,  314,  345 

Attributes,  and  'things,'  214,  253  ; 
connoted,  248  ;  denoted,  256-257 

Average  function  and  logical  char- 
acter, 187,  242-244,  255,  275- 
277 

Axioms,  as  foundation  lor  Logic,  6, 
23,  39,  95  ;  (examj»les.  21,  102- 
103,  159  tf.);  in  Geometry,  33 
tf. ;  formation  and  use  of,  115 

li.iin,  A.,  names  of  substances,  251 
,1.  ;  abstract  names,  254  -  255  ; 
essential  projjositions,  269 

Baker,  G.  P.,  55  n.,  76 

Benecke,  E.  C,  248  n. 

Bosanquet,  B.,  j»ractical  asjtect  of 
Logic,  6  n.  ;  nature  of  inference, 
111  n.,  125  ;  an  examjJe  (quoted, 
128  n.  ;  imi>erfect  knowledge, 
230  ;  hyi>othetical  propositions, 
274  /«.;  predication,  295  n.  ;  im- 
mediate inference,  304 

Bradley,  F.  H.,  tautology,  36  ;  fonns 
of  argument,  65  w.,  72  ?/.  ;  in- 
ductive methods,  95  v.  ;  •  intelli- 
gent doubt,'  224  n. ;  '  connotation,' 
245  M. 

Casuistry,  excessive  dislike  of,  125, 
215-216,  222-223  ;  importance  of, 
25  tf.,  35,  193,  233-234  ;  com- 
pared with  experimentation,  217 


36G 


USE  OF  \rORDS  IX  REASONING 


INDEX 


o 


67 


Categorical  and  Hyi»othetical,  detect.-? 
of  the  distinction,  '11  J.  tl".,  liSO  : 
as  assertion  of  fact  and  of  rule, 

275  ;  as  ini|»lying  existence  of  S, 

276  ;  as  minor  and  major  premiss, 
276-279  :  as  abstractions  from  the 
syUo^asm,  277  ;  as  a  distinction 
among  syllogisms,  289  \\. 

Cause,  the  notion  as  needed  for 
Logic,  60,  61,  72-73,  87,  100  ff. ; 
immediate  se<iuence,  92,  104  ;  un- 
conditional or  invariable  setjuencc, 
102-104,  106 

Causal  and  empirical  law,  91,  105, 
287 

Change  of  meaning,  due  to  new  dis- 
coveries, 43,  156,  164,  248,  and 
§  49  ;  as  source  of  verbal  contra- 
diction, 152,  162,  161  ;  fading 
of  metaphor,  168 

Circumstances,  'single,'  67,  94  ff., 
173  ;  disjointed  conception  of, 
101-104,  135  ;  familiarity  of,  105. 
114 

Circular  reasoning  and  definition, 
examples  of,  34 H  n. 

Class,  meaning  of  the  word,  149  ff.  ; 
always  a  sect,  152-157;  need  for 
subdivision,  196-197,  234  ;  older 
and  newer  conception,  151  ff. , 
165,  167  ;  natural  and  artificial, 
152-157  ;  de|)ends  on  essential 
resemblance,  157,  167,  169;  in- 
volves individual  difference,  69, 
157,  166,  174  ff. ;  not  prior  to  the 
definition,  248 

Class-name  (or  General  name),  com- 
{lared  with  pro|)er  name,  242, 
247,  249  If.  ;  com]>ared  with  meta- 
phorical name,  167  ff. ;  cora[>are4l 
with  descriptive  name,  250  ;  its 
connotation,  244  ff.,  25 1  ;  its 
indefiiiiteness,  174  ff.,  185,  194  ; 
the  instrument  of  description, 
142,  145,  227  ;  limits  of  its 
descriptive  force,  165,  170,  172, 
175,  227;  'correct*  meaning 
illusory,  158-164  ;  varieties  of 
correct  meaning,  167,  252 

Common  Sense,  its  relation  to  science, 
24  ff. ;  its  suspicion  of  philosophy, 
124.  154,  176,  179,  IPS  ;  com- 
|>ared  with  traditional  Logic.  46, 
184,  197,  270  ;  its  nee<l  of  more 
careful  Logic,  16,  56,  70,  74,  156. 
243,  270 


Complexity,  in  jireilicate  term,  63  ff. . 

143;  in  facts,  67,  94  ff.,  173,  207; 

as  source  of  ambiguity.  66,  75 
Conception,      compared      with     de- 

scriittion,   141  n.\  coniiiared  with 

interiiretation,    145    ff.  ;    and  see 

Miscoiicejtlioii 
Conclusion,   sup|»orted   by   facts,   59 

tf.,  81,  118;  relation  to  premlsso. 

61  ff.,  72,  82,  132,   277  ;    lack  of 

finality,  68,  82,  88,  106,  231  ;  ;i.s 

arbitrary  end,  119,  173 
ConuoUition,   as  intended   by  .1.    S. 

Mill,  245  ff. ;  as  list  of  conditions. 

not  group    of  qualities,   248  ;    as 

definition,   249,   252  ;  of  abstract 

names,   257  ;   of  attributes,   248  . 

of  pro[>er  names,   247  ;    mistake.^ 

about,  245  w.,  246-248,  257 
Connotative    as    'descriptive,'    lM:', 

249,  250 
*  Conjunction  '  asserted   and  denied, 

28*2,  294  M. 
Consequent     clause      mistaken     for 

hyi»othetical,  274 
Context,  neglected  by  Formal  Logic, 

240  ff.,  259,   273,  287  ;  examples 

of  its  use,  185,  187-188,  251-255. 

261,  269,  275-'277,  283 
Contradiction,    merely    verbal,     43. 

156,   162,    164,   248  ;   (examples. 

100,    I'JO,    152,    161):     Uw   of. 

162 
Conversion,  belongs  to  sentence  only. 

278-279  ;     its   small    im[)ortance, 

302-304 
Copula,     in     negative    profwsitions. 

263    ff. ;    as   sign  of   predication. 

266 
'  Correct '    meaning,   as    barrier    for 

thought,    158-164  ;    varieties   of. 

167,  252 
Criticism,  mingled  with  a  judgment. 

116;  its  two  poiuta  of  attick,  82. 

122-124;  129  ff. 

Deduction,  contrasted  with  induc- 
tion, 286  ff, :  ;ia  interpretation  of 
sentences,  13,  286-287,  300  :  'for 
the  sake  of  argimient,'  116,  132, 
289 

Definition  (and  Distinction),  different 
sorts  of,  42,  252;  and  "  transU- 
tiou,'  47  ff. ;  abstract,  49,  10!'.. 
110,  161  ;  *ime  as  connotation. 
249  ;  cannot  alter  tact;  111,  lit. 


161  ;  prior  to  class,  248  ;  lack  of 
finality,  7,  175,  177-178,  194, 
218  ;  changed  through  new  dis- 
covery, 43,  156,  164,  248,  and 
§i  49  ;  '  sutticient,'  176,  194  ;  in 
siK?cial  context,  20  ff.,  43-44,  201  ; 
importance  of,  136-137,  174  ff., 
193,  219  rt.  ;  demand  for,  188, 
193,  197,  202-203,  212,  250; 
baffled  search  for,  218  ;  of  techni- 
calities, 5,  28,  41  ff.,  50,  51  ;  in 
Geometry,  33,  42  ;  of  natural 
clas.ses,  152-157  ;  circular.  34 S  /i.  ; 
questions  of.  205  tf. 

Degree  of  indeliniteness,  180  tl.,  198- 
199,  207 

De  Morgan,  A.,  treatment  of  ellipti- 
cal arguments,  78  n.  ;  quality  of 
pro|K)sitions,  267  m.  ;  rules  of  the 
Syllogism,  297 

DenoUition,  252  ;  ot  attributes,  256- 


257 


I)escription.  conq  wired  with  con- 
ception, 123,  141  /'.  :  same  as 
l»redication,  or  statement  of  fact. 
142,  145  tf.  ;  complexity  of,  143  ; 
ijy  metaphor,  142,  167  tf.  ;  defects 
of,  149,  161-169,  17  t  tl. 

Descriptive  name,  same  as  *  connota- 
tive,' 245,  249,  250  ;  has  defects 
of  class- name,  142,  145,  and  see 
Class-nam*: 

Difference,  '  e.s.seiitial,'  35,  157,  167, 
169;  individual,  122-123,  165- 
167,  175  ;  method  of,  90-96,  107 

Distinction,  see  Definition 

Doubt,  its  practical  limits,  101,  233  ; 
its  partial  character,  229,  232  ; 
unimportant  when  idle,  108-109, 
176,  195  ;  indirectly  assertive, 
224-226;  of  'valid'  .syllogism. 
82,  133-134;  of  inductive  'con- 
clusion,' 88,  93-95,  102-106,  120: 
of  jiredieative  statements,  165- 
167,  169,  171  -173,  212-214  ; 
whether  'A'  is  A,  111,  160-162, 
228  ;  due  to  defects  of  language, 
99-100,  227-228  ;  its  function  in 
judgment,  29,  35,  96,  115-117, 
122,  229,  231 

Kmpirical  law,  91,  105,  287 
E« [national  syllogisms,  72  n. 
K(iuivocal  terms,  182,  185,  207,212 
Essence,  older   and  newer  view  of, 
152,  165,  167 


Essential,  resemblance  and  ditfer- 
ence,  35,  120,  152,  157,  167,  169, 
173  ;  propositions,  269  If.  ;  con- 
nections, 103-107,  124,  148 

Exceptions,  imjM>rtance  of,  25  tf. . 
35,  60,  193,  227 

Existence  of  S,  276 

Exj)eriment,  use  of,  S^,  135-136, 
217 

I'act,  relevance  to  conclusion,  60, 
69,  79,  86,  133-134,  148  ;  rela- 
tion to  theory,  6:*,  129-131,  147, 
165,  227,  358  tf.  ;  conception  and 
interpretation  of,  145  ff.  ;  mis- 
conception and  its  results,  94, 
106-107,  126,  147-148;  'single- 
ness' of,  67,  94,  173;  need  for 
analy.sis  of,  66,  69,  75,  96,  117  ; 
'bareness'  of,  99,  147;  need  for 
reconsideration  of,  127,  130,  136, 
173,  288-289;  questions  of,  86, 
205  tf.  ;  not  settled  by  definition. 
Ill,  114,  161 

Fallacy,  syllogistic,  12-15,  82,  133. 
297-300 ;  inductive,  94,  97-98. 
107 

Function  determines  logical  char- 
acter, 187,  241  ff,  255,  275-277 

(ieneralisation,  its  use  in  rea.soning, 
24,  6'2,  73,  129-131,  276;  its 
grounds,  chap.  iii.  ;  its  reference 
to  jmrticular  cases,  36,  44,  and 
see  Abstract  stutenients 

General  name,  see  Chiss-namc 

Geometrical  axioms,  33  ff. 

Grammar  confused  with  Logic,  19, 
240-244,  250,  253,  265,  273, 
286-287,  290 

'Half-truths,'    25     ff.  ;    in    .science 
generally,    27  -  30,    35,     88,     99. 
107  ;  in  Logic,  39-41,  44-47 
Herschel,  inductive  methods,  89 
Hurried  judgments,  28,  54,  112,  208 
HyiK)thesis,  use  of,  35,  %^,  116-117, 

'132,  289 
Hyi)othetical  projiosition,  confused 
account  of,  273-274  ;  order  of  its 
clauses,  273,  278,  297 ;  distin- 
guished from  conditional,  291  ;  as 
major  premiss,  276-278,  290,  293 

Identity,  Law  of,  159-162 
Immediacy  of  sequence,  92,  104 


368 


USE  OF  WORDS  IN  HEASONING 


INDEX 


369 


Immediate  Inieience,  301  tl". 

Indetiniteness,    compared    with    am- 
biguity,   178   tf .  ;  degrees  of,  180    ; 
ff.,  198-199,  i>07  ;  ami  subdivision   j 
of  classes,    196-197,    li34  ;   of  all 
descriptive    names,    174    ff.,    185, 
194 

Induction  and  deduction,  286  tf. 

Inductive  methods,  nature  of,  89  tf.  ; 
use  of,  9f)  tf.  ;  formality  of,  9,  10, 
92-95,  97,  101  n.,  107  ;  'con- 
clusion' from,  88,  lOG,  119,  171, 
173 

Inference,  see  Rfusiniiivj 

Inferential  pro|K>sition,  277,  293  ; 
its  contrapositive  forms,  278 

Instinct  and  Reason,  112  tf. 

Interjirctation  of  sentences,  deduction 
as,  13,  286-287,  300  ;  ditticulties 
neglecte<l  by  Formal  Logic,  20, 
259  tf.,  263,  and  see  Conttxt ;  fixed 
ndes  for,  19,  283,  303,  305 

Invariable  soiiucnce,  102-104 

.lames,  AV.,  Reason  in  animals,  113  ; 
meaning  of  '  essence,'  167  n. 

Jevons,  W.  S.,  Substitution  of 
Similai-s,  21,  23,  35,  102,  160: 
equational  syllogisms,  72  n.  ; 
logical  machine,  79  //.  ;  Method 
of  Ditference,  93  vi.  ;  examples  of 
'ambiguity,'  184  n.  ;  connotation, 
245  H.,  247  ;  'substantial  terms,' 
251  ;  Subject  and  Predicate,  260  7i. 

.Johnson,  W.  E.,  hyjwthetical  pro- 
positions, 280  -  283,  291  -  294  : 
rules  of  the  Syllogism    297 

Jones,  K.  E.  C,  novelty  in  con- 
clusions, 59  /*. 

Judgment,  as  a  growth,  117-121 
135,  305  ;  its  dej»endence  on 
previous  judgment,  65-66,  86,  89, 
96,  98,  123  ;  as  i>rocess  and  as 
instrument,  115  tf.  ;  as  choice 
between  yes  and  no,  115,  172, 
226-227  ;  function  of  doubt  in, 
29,  35,  96,  115-117,  122,  229, 
231  ;  promptness  of,  54,  112- 
113,  208  ;  correction  only  j»artial, 
229,  232 

Keynes,  .1.  N.,  neglect  of  context, 
239  ;  general  and  singular  names, 
251  n.  ;  abstract  and  concrete 
names,  254  ;  positive  and  negative 
names,     268     n.  \     essential    and 


accidental  pro|»ositiou.s,  269  <^  : 
eonnotation,  271  n.  :  hyi>otheti 
cals,  272  It.  ;  nuxiality,  279  n.  ; 
categorical  and  other  syllogisms, 
291-300;  AAO  in  fourth  Fig., 
298  ;  functions  of  language,  441  //. 

Kinds,  natural,  152-157 

Knox,  H.  v.,  (Jreen's  philosophy, 
184  n. 

Language,  in  relation  to  Thought, 
see  I  fcacription  and  D<riptiv»: 
nniiu' 

Laws  of  Thought,  1.'>1<  tl.,  Jj.'i 

•  Lewis  Carroll,'  negative  terms,  266  : 
'a  logical  paradox,*  2h3  n. 

'  Likeness,'  vagueness  of,  21,  23, 
and  sec  Essmtial  nstrnhfauo: 

Logic,  main  purpose,  3-7,  121  ; 
j»ractical  asj>ect,  46,  47  /'.  ;  pro- 
gressive character,  6,  39-46,  50, 
53-54,  99  ;  relation  to  common 
sense,  16,  56,  70.  74,  156, 
174,  184,  243,  270:  'scien- 
titic'  and  other,  4,  46.  51,  88, 
109,  208  :  its  foundation  on 
axioms,  6,  23,  39,  9;''  :  restric- 
tions of  province,  8-9,  127,  322 
tr.  ;  de<luctive  and  inductive,  9 
101,  286  If.  ;  its  relation  to  con- 
troversy, 55,  85,  l28n.  ;  its 
relation  to  psychology,  9,  120  ; 
symlK.lic,  281  tf.,  2a8-289,  293: 
tbrmal,  chap.  xii.  :  ditticulties  of 
teaching,  50  tf.,  and  chap.  xiii. 

Logical  chara<ter.  187,  239  If.  2.'.', 
275,  277 

Logical  form,  11,  144,  •J59  265,  303 

Logical  proof,  68,  82,  231,  and  see 
( 'onrhtsiofi 

Lotze,  negative  projwsitions,  265-266 

Major  j>remi.ss,  as  general  rule,  62, 
73,  81,  86,  129-131  :  as  hyiK)- 
thetical,  276-278,  290,  293; 
complexity  of,  63  tf.  :  uncouth 
forms  of,  65  n.  ;  implied,  76  tf.  ; 
how  reached,  87  tf. 

Mathematics  as  tyjKj  of  science,  4, 

33,  35,  39,  288 
Matter-of-fact  description,  142,  167 

tr. 

Meaning,  and  application,  10,  22  tl. , 
36,  92,  130  :  'correct.'  158,  164, 
167.    252  :  changed   by   new  dis- 


covery, 43,  156,  164,  248  ; 
tluctuation.<  of,  213-214;  de- 
stroyed by  ambiguity,  188,  201  : 
irreducible  minimum,  283  ;  ques- 
tions of.  205  tf. 

Mechanical  rules,  etfect  of,  13  v., 
74,  79,  83,  85,  97,  126-127,  328 

Metaphorical  description,  142,  167  tV. 

Middle  term,  nature  of,  66  /*.,  228, 
250;  ambiguity  of,  66-71,  75, 
82-84,  133-134,  286;  analysis  of, 
6Q,    69,    75:    undistributed,    14, 

29  7 -'299 
Mill,  J.  S.,  inductive  methods,   89- 

98,107;  causation,  100-104;  natu- 
ral kinds,  155  ;  connotation,  245, 
217,  257  :  negative  co[)ula,  264, 
266  ;  verbal  an<l  real  jtrojiositions, 
269  ;  hypothetical  projM)sitions, 
274  ?f,;  '  ]»articulars  to  particulars,' 

30  : 
Minor  picnii.ss,  as  lact  prtxiuced,  63  ; 

relevance  of,  60,  69,  79,  86,  133- 
134,  148;  complexity  of,  63  tf., 
143  ;  as  predication,  135,  276,  295    i 

Misconception  of  fact,  94,  106-107, 
126,  147-148,  227,  '232 

Moilality.  279  tf. 

Nauic,  kinds  of,  239  tf. 
Natural  kinds,  152-157 
Negation,  263  tf. 

Ob  version,  264,  302 

■  Particular"  proposition,  2»jw 

'  Particulars  to  particulars,'  123-124. 

304 
Pet  it  10  Principii,  see  Qiicstion-heifginij 
Po^f.  hoc,  profiler  hot-,  90  n.,  98 
Practice  and  Theory,  24,  47  ?^,  100- 

101,  and  see  Applicatlov 
Practical  pur]>08es,  variety  ot,    190, 

231 
Predicables,  152,  326 
Predication,  same  as  description,  1 12, 
145  ff.  ;  asserts  essential  resem- 
blance {i.e.  involves  i»uri»ose),l33- 
134,  142,  157,  165-167,  169, 
173,  203,  277  ;  by  meU]»hor,14'2, 
167  tf.  ;  whv  doubtful,  165-167, 
169,  171-173,  212-214  ;  as  minor 
[•remiss,  35,  276,  295  ;  lays  em- 
phasis on  predicate  term,  144,172, 
262,  295  :  ditticulties  in  detining, 

272  tr. 


Premisses ;  a.'?  abstractions  from 
Syllogism,  277  ;  no  priority  to 
conclusion,  61  tf.,  72,  82,  132  ; 
as  points  of  attack,  122  :  false 
duality  of,  129  tf.  ;  etfect  of  com- 
bining, 133-134  ;  conversion  of, 
279,  302  ;  misinterpretation  of,  14, 
300.     See  also  Major,  and  Miliar 

Previous  knowledge,  importance  of, 
65-66,  86,  89,  96,  98,  123 

Progress  of  knowledge,  in  general, 
chap.  viii.  ;  the  normal  condition, 
25-30,  171-173  ;  involves  present 
incompleteness,  102,  161  -  162, 
231  ;  involves  change  in  detini- 
tions,  44,  218,  248  ;  due  to  search 
for  exceptions.  28,  31,  35,  130, 
193,  218;  hindrances  to,  211, 
215,  219,  an.l  §  68 

Proof,  as  gradual  elimination  of 
error,  29,  30,  54,  88,  289  ;  logical, 
^S,  82,  231,  and  see  ConcJusion 

Proper  name,  com{>ared  with  general 
name,  242,  247,   249  tf.  ;  used  :is 
general,  168-171,  255;  and 'con 
notation,'  247 

•  Proposition,'  defects  of  the  word, 
17  «.,  and  see  Assertion  ;  'one' 
and  'more  than  one,' 117,  143, 
273,  301 

Proverbs  as  half-truths,  26,  46 

Purpo.so,  determines  'es.sence,'  35, 
120.  167,  175-176  ;  in  predica- 
tion, 133-134,  148  //.,  157,  203, 
352  ;  in  proof,  106,  109,  231 

<,»ue.stions   of  fact   and   of  meaning, 

205  tl. 
Question-begging,  131  tf.  ;    examples 

of,  348  V. 

Read,  C,  formal  induction,  10  v.\ 
Method  of  Ditference,  93  n.,  108  ; 
negative  copula,  264  n. 

Real  and  verbal  propositions,  269  n. 

Reality,  knowledge  of,  229,  and 
see  Doubt 

Reasoning,  process  and  subject- 
matter,  9  tf.,  314,  3'22-325,  327- 
329,  354,  362-363  ;  reflective,  58, 
81,  116-117.  119,  132;  from  given 
juemisses,  75  ?t.,  80,  128,  288- 
289,  315  ;  to  new  conclusion,  117 
ti'.,  128,  and  see  Progress  of  knov- 
Icdge ;  without  words,  112,  123; 
its  need  of  generalisations  24,  62, 


24 


I 


370 


USE  OF  WOEUS  jy  JiEASOMMi 


73,  129-131,  JTt)  ;  its  need  oi 
analysis,  65,  69,  75,  96,  117: 
definition  of,  chap.  iv.  See  also 
ConeltLsion,  Doubf,  J'remisses,  and 
frmtf 

Reduction  to  first  Fig.,  279,  302 

Relevance  of  minor  jiremiss,  60.  61*. 
79,  86,  133-134,  148 

Rol)€rtson,  ('».  C. .  72  //. 

Rults,  niechanieal,  13  /^,  74,  79.  >  :. 
85,  97,  126-127,  328 

Scepticism,  see  Doubt 

Science,  its  relation  to  common - 
sense,  24  t\.  ;  its  general  aim,  28, 
30  ;  mathematical  conception  of, 
4,  33,  36,  39,  288  :  its  tisi-  of 
hypothesis,  35,  8S,  116-117,  132, 
289:  its  interest  in  exceptions,  28, 
60  61,  193:  its  lack  of  finality, 
29,  88,  99,  106-108,  161-162, 
171,  and  chap.  viii. 

Sentence  lonfuscd  with  as.sertion,l  7- 
19;  chief  consequences,  345  n. 

Shifty  a.sstrtion,  36,  203,  219, 
220 

'Simple  enum<ration,'  87  »,,  [iQ  n.. 
97 

'Single,'  ciri'Uin>tame,  61,  !<4  If.. 
173  ;  prnpixitioii.  117.  14-5.  27:'. 
301 

Singular,  name,  251,  257  ;  ]»roj>osi- 
tion,  363 

'So-called  A,'  111-112,  160 

S|>encer,  H.,  79  n. 

Stout,  (}.  F.,  262 

Subject  and  rrt-dicate,  dillirulty  of 
distinguishing,  144,  260-262, 
295  :  existence  of  S,  276  ;  iu- 
definiteness  of  S,  255,  262,  295. 
For  nature  of  P,  see  Predication 

Subject-matter,  see  Reasoning 

Substitution  of  Similars,  21.  a.'>,  102. 
159,  160 

Sully,  J.,  40  /t. 

Syllogism,  in  general,  58  ll.,  122  ; 
contrasted  with  '  propositional 
synthesis,'  294  :  as txpanded  con- 
clusion, 82,  132,  177  ;  typical 
form,  62.  81,  278-279,  302  ;  cate- 
gorical and  other,  289  tl.  ;  uses 
of,  71  tf.:  rules  of,  269  tf.  :  as 
petitio  principii,    131    tt.  ;     valid 


and  invalid  forms,  11-15;  uutoulh 
forms,  65  w. ;  '  equatioual,'  72  n. 
Symboli<-   Logic,    2h1     H.,    288-289. 
293 

Technicalities,  puri>ose  of,  5,  28,  41 
tf.,  50-51 

Theory,  its  relaliuu  U>  larl,  -5,  1^9- 
131,  147,  165,  227,  358  If.  ;  its 
relation  to  practice,  24,  47  a.,  100- 
101,  and  see  Apj'iication  ;  ap|»eal 
to  previou.s,  65-66,  86,  89  fl'.,  96, 
9S,   123 

'Things,"  214,  253 

*  Translation,'  47  tf. 

Tiuism  as  refuge  in  controv.  r-^v.  oO- 
39 

Truth,  its  relation  to  practice,  24, 
17  »..  100-101  ;  claimed  in  all 
a.ssertion,  281,  284;  as  a  challenge, 
100;  definition  of,  105,  218;  its 
tle|)endence  on  statement.  2*^.  227- 
228,  .nid  see  ^ciaicc 

Unciinditional     se«iuence,      102    //.. 

104,  106 
rndistribute<l  Middle,  1  I,  297-299 
Uniformity  of  Nature,  102  tf. 
Universal    ami    Tarticular     prop.- 

tions,  263  i\\ 
Univocal  and  equivocal   tenns,  182, 

185,  207,  212 

*  Validity  '  of  rea.soning,  11-15 
Venn,  .).,  .Mill's  inductive  niethmls, 

95  /I.  ;  negative   copula,    264    n.; 

essential      propositions,     269     w.; 

iiMMlalitv,  280  tl. 
Verbal  disputes,  205  ff. 
Verification,  89  If.,  9S 

Ward,  .1.,  Uniluimity  of  Nature,  73 
/<. ;  origin  of  life,  158  w. 

Watson,  J.,  234 

Whately,  inductive  Logic,  9  ;  reason- 
ing and  judgment.  111  h.,  125, 
and  126  ' 

Words,  as  instruments  of  a.ssei  tion, 
142,  241  tf.,  255  ;  as  hindrance 
to  thought,  158-164  ;  as  source  of 
error,  66-71,  75,  82-84,  94,  123, 
133-134,  136-137,  141,  146, 
227 


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